# Math worksheet for Speed and Rate sums

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Speed and Distance sums

1) Sam walked from village B to village A at constant speed of 60 m/min.
Tom and Vivian walked from village B to Village A at constant speeds of 50 m/min and 40 m/min respectively.
All three children started their journey at the same time. Sam first met Tom. 10 minutes later, he met Vivian. Find the distance between the two villages.

Ans :- 11 km

2) Ann and Bella were cycling around a 10 km circular track at constant speeds of 30 km/h and 20 km/h respectively.
They began at the starting line at the same time but cycled in opposite directions.
(i) How long would it take for Ann to meet Bella for the 1st time?
ii) How long would it take for Ann to meet Bella for 3rd time?

Ans :- i) 1 h
b) 35
h

3) Jill and Sam were walking around a 400 m circular track at constant speeds of 50 m/min and 30 m/min respectively.
They began at the starting line at the same time but walked in opposite directions.
(i) How long would it take for Jill to meet Sam for 5th time?
(ii) How far would Jill have walked when he met Sam then?

Ans :- i) 25 minutes
ii) 1250 m

4) Two marbles were released at the same time and they started to roll towards each other from the opposite ends of a straight plank that was 380 cm long. Marble A travelled 70 cm while Marble B travelled 40 cm in the first second. Both marbles travelled 5 cm less than the previous distance in each subsequent second. How long did it take for the two marbles to meet?

Ans :- 4 seconds .

5) Mary and Ben took 49 hours to complete their science project. They worked separately on their own project. If Mary had worked 5 hours less and Ben had worked 6 hours more, Mary would have put in 2 hours more than Ben. How many hours did Mary put in for the science project?

Ans :- 31h.

6) Sue drove past Orchard Mall travelling at an average speed of 80 km/h to Maple Mall. Derek left Orchard Mall one hour earlier than Sue and took 5 hours to reach Maple Mall, travelling at an average speed of 72 km/h. Derek reached Maple Mall at 6 p.m.
(a) At what time did Sue leave Orchard Mall?
(b) How far was Sue from Maple Mall when Derek reached the destination?

Ans :- a) 2 pm
b) 40 km .

7) Sunshine City and Moon Town were 361 km apart. At 06 00, Azman started travelling from Sunshine City to Moon Town at a constant speed of 80 km/h. 45 minutes later, Baoming left Moon Town and travelled towards Sunshine City at a constant speed of 60 km/h. at what time did Azman and Baoming pass each other?

Ans :- 2910 h.

8) A bus which left Terminal Y, was scheduled to reach Terminal Z at a certain time. After travelling for an hour at its usual speed, the bus stopped for 30 minutes due to an engine problem. In order to reach Terminal Z at the scheduled time, the bus travelled the remaining journey at a speed which was 6 km/h faster than the usual speed. The bus took 4 hours to cover the remaining journey.
(a) Find the usual speed of the bus.
(b) Find the distance between the two terminals.

Ans :- a) 48 km/h
b) 264 km .

9) Devi and Laura took part in a cycling competition. Devi's average speed was 400 m/min. When Devi completed the journey in 45 minutes, Laura still had 900 metres to cover.
a) What was the distance of the cycling competition?
b) What was Laura's average speed?

Ans :- a) 18000 m
b) 380 m/min .

10) Town A and Town B were 395 km apart. At 6 a.m., a car started travelling from Town A to Town B at a constant speed of 60 km/h at 6.20 a.m., a motorcycle started travelling from Town B to Town A at a constant speed of 90 km/h.
a) At what time did they pass each other?
b) How far away was the car from Town B when it passed the motorcycle?

Ans :- a) 8.50 am
b) 225 km .

11) Mingfa cycled from Town A to Town B. He cycled 49 of the distance in the 1st hour, 13 of the distance in the second hour and the remaining distance in the third hour. His average speed for the first two hours was 10½ km/h. Find his average speed for the whole journey.

Ans :- 9 km/h.