A takes 8 hours more than the time taken by B to cover a distance of 160 km. If A doubles his speed, he takes 3 hours more than B to cover the same distance. The speed (in km/h) of is:
Answer & explanation
Correct answer: option 4
Let speed of A = A km/h
Speed of B = B km/h
According to question ,
\(\frac{160}{A}\) - \(\frac{160}{B}\) = 8 ------(1)
\(\frac{160}{2A}\) - \(\frac{160}{B}\) = 3
\(\frac{80}{A}\) - \(\frac{160}{B}\) = 3 --------(2)
Multiply equation (1) by \(\frac{1}{2}\)
\(\frac{80}{A}\) - \(\frac{80}{B}\) = 4 -----(3)
\(\frac{80}{A}\) = 4 + \(\frac{80}{B}\)
Put in (2)
4 + \(\frac{80}{B}\) - \(\frac{160}{B}\) = 3
On solving B = 80 km/h
So , Speed of B is 80 km/h