Question

In covering a distance of 30 km, A takes 2 hours more than B. If A doubles his speed, then he would take 1 hour less than B. A's speed is:

A. 5 km/h

B. 8 km/h

C. 10 km/h

D. 15 km/h

Answer 1

A. 5 km/h
=================================
Distance = 30 km

Let the Speed of A be x and that of B be y

x = 30/t₁
t₁ = 30/x

y = 30/t₂
t₂ = t₁-2
t₂ = (30/x)-2
(30/y) = (30-2x)/x
y = (30x)/(30-2x)
y = (15x)/(15-x)
________________
2x = 30/t₃
y = 30/t₄
t₃ = 15/x

t₄ = t₃+1
t₄ = (15/x)+1

(30/y) = (15+x)/x
y = 30x/(15+x)
________________
(30x)/(30-2x) = (30x)/(15+x)

30-2x = 15+x
3x = 15
x = 5
-----------------------------
Hence the speed of A is 5 km/hr
=======================