► Speed and Distance sums
1) Tom and Gary ran in race. When Tom had completed the run in 20 minutes, Gary had only run 5⁄8 of the distance. Gary's average speed for the race was 75 m/min less than Tom's.
i. Find the distance of the race.
ii. What was Gary's speed in m/min?
Ans :- i) 4000m
ii) Gary's speed was 125 m/min.
2) James and Kevin took part in a cross-country race. When Kevin had completed the race in 30 minutes, James had only 7⁄10 of the distance. Kevin's average speed for the race was 45 m/min faster than James'.
i. Find the distance of the race.
ii. What was James' speed in m/min?
Ans :- i) 4500 m
ii) James' speed was 105 m/min
3) At 8 am, Allen and Bob started their morning jog from their house to a nearby park. Allen jogged at an average speed of 150 m/min while Bob's average speed was 100 m/min. After arriving at the park, Allen rested for 10 min and jogged back home. Allen met Bob at 8:40 am on his return journey, find the distance between their house and the park.
Ans :- 4250 m
4)Town A is 100 km away from town B. Tom cycled the first 40 km at an average speed of 20km/h. He cycled the next 40 km at an average speed of 30 km/h. If he wanted his average speed for the entire journey to be 25 km/h, at what speed must he cycle the remaining journey?
Ans :- 30 km/h
5) Two cars A and B travel from X to town Y at uniform speeds of 60km/h and 80 km/h respectively. When they start their journey, car A is 15 km ahead of car B.
i. How long does it take for car B to catch up with car A?
ii. How long does it take for car B to be 25 km ahead of car A?
Ans :- i) 3⁄4 h
ii) 2 h
6) A lorry and a coach were travelling from A to B at average speeds of 80 km/h and 100 km/h respectively.
At 9 am, the lorry was 60 km ahead of the coach. Half an hour later, the lorry stopped for breakfast.
i. How far was the lorry ahead of the coach when it stopped for breakfast?
When the coach passed the lorry, the lorry driver was still having breakfast.
ii. At what time did coach pass the lorry? (10 am)
Ans :- i) 50 km
ii) The coached pass the lorry at 10 am
7) At 6 am, Ann traveled at a constant speed of 90 km/h from town A to town B. At 7:30 am, Bob also left town A for town B traveling at a constant speed. At 12:30 pm, Bob overtook Ann.
i ) Find the speed of Bob. How much faster was Bob than Ann? ii) After Bob overtook Ann, he reached town B 1 2⁄3 hour later. How far away was Ann from town B then? (1 step only!)
Ans :- i)Bob's speed was 117 km/h and he was 27 km/h faster than Ann
ii) 45 km
8) At 12 pm, Alvin started to drive from town A to town B. Half an hour later, Ben also left town A for town B but he drove at a constant speed 20 km/h faster than Alvin's. When Ben started his journey, Alvin had already traveled 30 km.
i. What was Alvin's average speed?
ii. At what time did Ben catch up with Alvin?
Ans :- i) Alvin's average speed was 60km/h
ii) At 2 pm Ben catch up with Alvin.
9) Peter and John were cycling at constant speed from town A to town B. John started the journey 2 hours after Peter but he caught up with Peter 3 hour later. John was cycling 10 km/h faster than Peter.
i) When John started his journey, how far ahead was Peter?
ii) Find Peter's speed. Find John's speed.
Ans :- i) 30 km
ii) Peter's speed was 15 km/h and John's speed was 25 km/h
10) Ahmad and Ben were driving at constant speed from town A to town B. Ben was driving 20 km/h faster than Ahmad. Ben started the journey half-an-hour after Ahmad but he caught up with Ahmad 1 ½ hour later.
i. Find the speed of Ahmad? (60 km/h)
ii. If both cars reached town B at the same time, find the distance between the two towns.
Ans :- i)Ahmad's speed was 60 km/h
b) Distance between the two towns is 120 km
11) A car took 8 h to complete the last ¼ of a journey at an average speed of 50 km/h. Its average speed for the whole journey was 60 km/h. Find the time taken for the first ¾ of the journey.
Ans :- 18 h 40 min.