► Speed and Distance sums
1) When Kumar partners Bala, they take 8 days to paint a house. When Bala partners Hashim they take 6 days to paint the house. When Hashim partners Muthu, they takes 12 days to paint the house. How many days do Kumar and Muthu takes to paint the house together?
Ans :- Kumar and Muthu take 24 days to paint house together.
2) Tom needs 20 hours to build a dinosaur model while Peter only needs 12 hours to do the same. After Tom has started building the model for 4 hours, Peter joins in. How much time do the two boys spend working together to build the model till completion?
Ans :- 6 hours
3) In a village, it was found that 20 mice ate 20kg of food in 20 days , and 3 cats caught 3 mice in 3 days. On average, how many kilograms of food did each cat save per days?
Ans :- 1⁄60kg.
4) Alan, Bob and Carl ran at a speed of 5km/h, 6km/h and 7km/h respectively. They ran along the same route and started at 6:00 am, 6:30 am and 7:00 am respectively. When Bob passed Alan, he gave Alan a message to pass to Carl. What time will Carl receive the message?
5) It takes 4 hours for 4 men to mow 100m² of field. It takes 6 hours for 3 boys to mow 90m² of field. At these rates, what is the total area of the field that 12 men and 12 boys can mow in 8 hours?
Ans :- 1080m²
6) John and Tom were at the beach. John had already collected 26 shells when Tom decided to collect as well. If John could collect 3 shells per minute and Tom could 4 shells per minute, after how long would there collection be the same?
Ans :- 26 minutes .
7) If a man jogs to his office from his house but drives back, he will take 5 hours. If he drives both ways, he will take only 3 hours.
i. How many hours will he take to jog both ways? (Assume that the jogging speed and driving speed do not change.)
ii. If his average jogging speed is 80 m/min, how far is his office from his house? (Give your answer in km.)
Ans :- i) He will take 7h
ii) 16.8 km
8) Sam jogged from town P to town Q at a constant speed. At 7 am, he was 20 km away from town Q. At 8:30 am, he was 8km away from town Q. What time did Sam reach town Q.
Ans :- Sam reached Town Q at 9.30 am .
9) Alice and Bethany left town X at the same time and traveled at constant speeds towards town Y. When Alice reached town Y, Bethany was still 80 km away. Bethany reached town Y 40 minutes later. If Bethany took 2 hours to reach town Y, find Alice's speed.
Ans :- Alice's speed is 180 km/h
10) A taxi and a car were traveling towards a town. The taxi overtook the car when they were 180 km away from the town. The taxi arrived at the town 45 minutes earlier than the car. When the taxi reached the town, the car was 60 km away.
i. Find the average speed of the car.
ii. Find the average speed of the taxi.
Ans :- i)The average speed of the car is 80 km/h
b) Average speed of taxi is 120 km/h 96 km/h.
11) A motorist took 2 h to travel from Town A to Town B. His average speed for the whole journey was 80 km/h. Fr the first ¼ of the journey, he travelled at an average speed of 60 km/h. Find his average speed for the remaining journey.
Ans :- 90 km/h.