QUESTIONS
Two inlet taps P and Q opened at the same time can fill a tank in 2 1/2 h. The two taps were opened together at the same time and after 1 hour 10 minutes tap Q was closed and P continued alone and filled the tank after a further 4 hours. Find:
a) The fraction of the tank filled by both taps for 1 hour. (1 marks)
b) The fraction of the tank filled by tap P after Q was closed. (2 marks) c) The time which each tap working alone would have taken to fill the tank. (7 marks) ANSWERS
If the bucket above has a hole and 1.1 cm3 of water leaks out every 5 seconds and collects in a cylindrical can of base radius and height 10 cm and 25 cm respectively. Calculate how long it takes to fill the cylindrical can. (4 marks)
RATES, RATIO, PROPORTION AND PERCENTAGE | RATES | FORM 1 LEVEL | PAPER 2 QUESTIONS | SECTION AA dam containing 4158m-cubed of water is to be drained. A pump is connected to a pipe of radius 3.5cm and the machine operates for 8 hours per day. Water flows through the pipe at the rate of 1.5m per second. Find the number of days it takes to drain the dam. (3mks)
RATES, RATIO, PROPORTION AND PERCENTAGE | RATES | FORM 3 | PAPER 2 QUESTIONS | SECTION AAtieno is now four times as old as her daughter and six times as old as her son. Twelve years from now, the sum of the ages of her daughter and son will differ from her age by 9 years. What is Atieno’s present age? (3mks)
From a reservoir, water flows through a cylindrical pipe of diameter 0.2m at a rate of 0.35m per second.(a) Determine the number of liters of water discharged from reservoir in one hour. (4mks)
(b) The water flows from the reservoir for 18 hours per day for 25 days per month and serves a population of 2500 families. Determine the average consumption of water per family per month giving your answer to the nearest 100 litres. (4mks)
(c) The water is charged at the rate of sh.4.50 per 100 litres. Calculate the average water bill per family per month. (2mks)
Form 2 Mathematics
A rectangular water tank measures 2.4 m long, 2 m wide and 1.5 m high. The tank contains some water up to a height of 0.45 m.
(a) Calculate the amount of water, in litres, needed to fill up the tank (b) An inlet pipe was opened and water let to flow into the tank at a rate of 10 litres per minute.After one hour, a drain pipe was opened and water allowed to flow out of the tank at a rate of 4 litres per minute. Calculate: (i) the height of water in the tank after 3 hours; (ii) the total time taken to fill up the tank.
answers
Form 1 Mathematics
Three workers, working 8 hours per day can complete a task in 5 days. Each worker is paid Ksh 40 per hour. Calculate the cost of hiring 5 workers if they work for 6 hours per day to complete the same task.
answer
Form 1 MathematicsPipe a can fill an empty water tank in 3 hours while, pipe B can fill the same tank in 6 hours, when the tank is full it can be emptied by pipe C in 8 hours. Pipes A and B are opened at the same time when the tank is empty. If one hour later, pipe C is also opened, find the total time taken to fill the tank (4 marks)
Answers
Form 2 Mathematics
A school water tank is in the shape of a frustum of a cone. The height of the tank is 7.2 m and the top and bottom radii are 6m and 12 m respectively.
(a) Calculate the area of the curved surface of the tank, correct to 2 decimal places. (b) Find the capacity of the tank, in litres, correct to the nearest litre. (c) On a certain day, the tank was filled with water. If the school has 500 students and each student uses an average of 40 litres of water per day, determine the number of days that the students would use the water.
answer
Form 1 Mathematics
An industrialist has 450 litres of a chemical which is 70% pure. He mixes it with a chemical of the same type but 90% pure so as to obtain a mixture which is 75% pure.
Find the amount of the 90% pure chemical used
Answer
Form 1 Mathematics
Eleven people can complete 3/5 of a certain job in 24 hours. Determine the time in hours, correct to 2 decimal places, that 7 people working at the same rate can
take to complete the remaining job.
answer
Form 1 Mathematics
Twenty five machines working at a rate of 9 hours per day can complete job in 16 days. A contractor intends to finish the job in 10days using similar machines
working at a rate of 12 hours per day. Find the number of machines the contractor requires to complete the job.
answer
Form 1 Mathematics
Two taps A and B can each fill an empty tank in 3 hours and 2 hours respectively. A drainage tap R can empty the full tank in 6 hours; taps A and R are opened for 5 hours then closed.
(a) Determine the fraction of the tank is still empty (b) Find how long it would take to fill the remaining fraction of the tank if all the three taps are opened
answer
Form 1 Mathematics
An inlet tap can fill an empty tank in 6 hours. It takes 10 hours to fill the tan kwhen the inlet tap and an outlet tap are both opened at the same time. Calculate
the time the outlet tap takes to empty the full tank when the inlet tap is closed.
answer
Form 1 Mathematics
A bus travels from Nairobi to Kakamega and back. The average speed from Nairobi to Kakamega is 80km/hr while that from Kakamega to Nairobi is 50km/hr, the fuel consumption is 0.35 litres per kilometer and at 80km/h, the consumption is 0.3 litres per kilometer .Find
Answer
​Related Questions and Answers on Speed and RatesForm 1 Mathematics
In January, Mambo donated 1/6th of his salary to a children's home while Simba donated 1/5th of his salary to the same children's home. Their total donation for
January was Ksh. 14 820. In February, Mambo donated 1/8th of his salary to the children's home while Simba donated 1/12th of his salary to the children's home. Their total donation for February was Ksh 8 675. Calculate Mambo 's monthly salary.
answer
Form 1 Mathematics
Five people can build 3 huts in 21 days. Find the number of people, working at the same rate that will build 6 similar huts in 15 days.
answer
Form 1 Mathematics
Kipketer can cultivate a piece of land in 7 hours while Wanjiku can do the same work in 5 hours. Find the time they would take to cultivate the piece of land when working together.
Answer:
Form 1 Mathematics
A water vendor has a tank of capacity 18900 litres. The tank is being filled with water from two pipe A and B which are closed immediately when the tank is full. Water flows at the rate of
a) If the tank is empty and the two pipes are opened at the same time, calculate the time it takes to fill the tank. b) On a certain day the vendor opened the two pipes A and B to fill the empty tank. After 25 minutes he opened the outlet to supply water to his customers at an average rate of 20 Liters per minute i) Calculate the time it took to fill the tank on that day. ii) The vendor supplied a total of 542 jerricans, each containing 25 litres of water , on the day. If the water that remained in the tank was 6 300 litres, calculate, in litres, the amount of water that was wasted.
answers
Form 1 Mathematics
In a certain commercial bank, customer may withdraw cash through one of the two tellers at the counter. On average, one teller takes 3 minutes while the other teller takes 5 minutes to serve a customer. If the two tellers start to serve the customers at the same time, find the shortest time it takes to serve 200 customers
answer
Form 1 Mathematics
A farmer feed every two cows on 480 Kg of hay for four days. The farmer has 20 160 Kg of hay which is just enough to feed his cows for 6 weeks. Find the number of cows in the farm.
answer
Form 1 Mathematics
a) The ratio of Juma's and Akinyi's earnings was 5:3 Juma's earnings rose to Ksh 8400 after an increase of 12%.
Calculate the percentage increase in Akinyi's earnings given that the sum of their new earnings was Ksh. 14100. b) Juma and Akinyi contributed all the new earnings to buy maize at Ksh 1175 per bag. The maize was then sold at Ksh 1762.50 per bag. The two shared all the money from the sales of the maize in the ratio of their contributions. Calculate the amount that Akinyi got.
answers
Form 1 Mathematics
A tank has two inlet taps P and Q and an outlet tap R. when empty, the tank can be filled by tap P alone in 4 ½ hours or by tap Q alone in 3 hours. When full, the tank can be emptied in 2 hours by tap R.
(a) The tank is initially empty. Find how long it would take to fill up the tank (i) If tap R is closed and taps P and Q are opened at the same time (ii) If all the three taps are opened at the same time (b) The tank is initially empty and the three taps are opened as follows P at 8.00 a.m Q at 8.45 a.m R at 9.00 a.m (i) Find the fraction of the tank that would be filled by 9.00 a.m (ii) Find the time the tank would be fully filled up
answers
A rectangular tank of base 2.4 m by 2.8 m and a height of 3 m contains 3,600 liters of water initially. Water flows into the tank at the rate of 0.5 litres per second. Calculate the time in hours and minutes, required to fill the tank ( 4 marks)MARKING SCHEME
A manufacture of jam has 720 kg of strawberry syrup and 800 kg of mango syrup for making two types of jam, grade A and B. Each types is made by mixing strawberry and mango syrups as follows:
MARKING SCHEME
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