Car ‘X’ travels for 4 hours to reach from point A to B. Car ‘Y’ travels at the…
2021
Car ‘X’ travels for 4 hours to reach from point A to B. Car ‘Y’ travels at the speed of 70 kmph to reach from point B to C in 3 hours. Distance travelled by car ‘X’ to cover point A to B is 1/7th more than distance travelled by car ‘Y’. How much time will car ‘X’ take to reach from point A to C?
- A.
9 hours
- B.
7.5 hours
- C.
5 hours
- D.
12 hours
- E.
15 hours
Attempted by 2 students.
Show answer & explanation
Correct answer: B
Concept
Speed, distance and time are linked by Distance = Speed × Time, so Time = Distance ÷ Speed. A phrase like “a is 1/7 more than b” means a = b × (1 + 1/7) = b × 8/7. To find the time for a whole journey, find the total distance of that journey and divide it by the speed of the car making it.
Application
Find Y’s distance (B to C): Y runs at 70 kmph for 3 hours, so distance = 70 × 3 = 210 km.
Find X’s distance (A to B): it is 1/7 more than Y’s 210 km, so A to B = 210 × 8/7 = 240 km.
Find X’s speed: X covers the 240 km from A to B in 4 hours, so speed of X = 240 ÷ 4 = 60 kmph.
Find the A to C distance: A to C = (A to B) + (B to C) = 240 + 210 = 450 km.
Find X’s time for A to C: time = 450 ÷ 60 = 7.5 hours.
Cross-check
Split the trip: A to B takes 240 ÷ 60 = 4 hours and B to C takes 210 ÷ 60 = 3.5 hours; 4 + 3.5 = 7.5 hours, which matches. So car X needs 7.5 hours to go from A to C.