Maths-
General
Easy

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 cross times time
    Distance covered by walking = 6cross timesx
    Distance covered by cycling = 2cross timesy
    We get 6 x equals 2 y not stretchy rightwards double arrow y equals 3 x — Eq1
    Given average cycling speed = 7km/hr faster than average walking speed
    not stretchy rightwards double arrow y equals x plus 7 — Eq2
    Step 2:- Eliminate y to get x
    Doing Eq1-Eq2 to eliminate y
    not stretchy rightwards double arrow y minus y equals left parenthesis 3 x right parenthesis minus left parenthesis x plus 7 right parenthesis
    not stretchy rightwards double arrow 0 equals 2 x minus 7
    not stretchy rightwards double arrow 2 x equals 7
    ∴ x = 3.5 kmph
    Step 3:- Substitute value of x in Eq2
    not stretchy rightwards double arrow y equals x plus 7 not stretchy rightwards double arrow y equals 3.5 plus 7
    ∴ y = 10.5 kmph
    ∴ Average walking speed is 3.5 kmph and average cycling speed is 10.5 kmph.

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