Question

# A man reaches a spot from his home in 6 hrs by walking, but he can reach the same spot from his home within 2 hrs by cycle. If the given average cycling speed is 7km/hr faster than his average walking speed, then find the average cycling and walking speeds.

Hint:

### let the average walking speed be x and average cycling speed be y.

Given average cycling speed = 7km/hr faster than average walking speed

As the distance between two places is same then equate distance covered by walking and distance covered by cycling

We get two equations then solve them to get the average cycling and walking speeds.

## The correct answer is: 10.5 kmph.

### Ans :- Average walking speed is 3.5 kmph and average cycling speed is 10.5 kmph.

Explanation :-

Step 1:- frame the equation from the given set of conditions .

let the average walking speed be x and average cycling speed be y.

Time taken by walking = 6 hrs

Time taken by cycling is 2hr .

As the distance between two places is same then equate distance covered by walking and distance covered by cycling

Distance = Avg. speed time

Distance covered by walking = 6x

Distance covered by cycling = 2y

We get — Eq1

Given average cycling speed = 7km/hr faster than average walking speed

— Eq2

Step 2:- Eliminate y to get x

Doing Eq1-Eq2 to eliminate y

∴ x = 3.5 kmph

Step 3:- Substitute value of x in Eq2

∴ y = 10.5 kmph

∴ Average walking speed is 3.5 kmph and average cycling speed is 10.5 kmph.

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