Speed of bike is 10% less than speed of car. The bike covers 180 km while the…
2021
Speed of bike is 10% less than speed of car. The bike covers 180 km while the car covers 300 km, and the car takes two hours more than the bike to complete its journey. Find the speed (in km/hr) of the bike?
- A.
50
- B.
45
- C.
36
- D.
54
- E.
27
Attempted by 4 students.
Show answer & explanation
Correct answer: B
Concept
Travel time equals distance divided by speed (t = d/s). When one speed is a fixed percentage of another, express both speeds with a single variable, then build one equation from the known gap between the two travel times.
Application
Let the car's speed be x km/hr. The bike is 10% slower, so the bike's speed is 0.9x km/hr.
Car travel time = 300/x hr. Bike travel time = 180/(0.9x) = 200/x hr.
The car's longer journey takes 2 hours more than the bike's, so 300/x − 200/x = 2.
100/x = 2, hence x = 50 km/hr (the car's speed).
Bike speed = 0.9 × 50 = 45 km/hr.
Cross-check
Car: 300/50 = 6 hr. Bike: 180/45 = 4 hr. The gap is exactly 2 hr, confirming a car speed of 50 km/hr and a bike speed of 45 km/hr.