A takes 2 hours more than B to cover a distance of 40 km. If A doubles his speed, he takes \(1\frac{1}{2}\) hour more than B to cover 80 km. To cover a distance of 120 km, how much time (in hours) will B take travelling at his same speed?

A takes 2 hours more than B to cover a distance of 40 km. If A doubles his speed, he takes \(1\frac{1}{2}\) hour more than B to cover 80 km. To cover a distance of 120 km, how much time (in hours) will B take travelling at his same speed? Correct Answer <span class="math-tex">\(1\frac{1}{2}\)</span>

Here, S₁ = x, S₂ = 2x (For A)

40 = 2x × x/(2x - x)

⇒ 40 = 2x(5/4)

⇒ x = 16

Actual time taken by A = 40/16 = 2.5 hours

Actual time taken by B = 2.5 -  2 = 0.5 hour

Speed of B = 40/0.5 = 80 km/h

Required time taken by B = 120/80 = 3/2 hours

Traditional method:

Given:

A takes 2 hours more than B to cover a distance of 40 km

When A doubles his speed, he takes 1.5 hours more than B to travel 80 km

Concept used:

Distance = Speed × Time

Calculation:

Let The speed B be x km/h.

Time taken by B to cover 40km = 40/x hour

Time taken by A to cover 40km = hour

Speed of A = (40)/ kmph

⇒ (20x)/(20 + x) kmph ……… (1)

Now,

Time taken by B to cover 80 km = 80/x hour

When A doubles his speed = (40x)/(20 + x) kmph

Time taken by A to cover 80 km = 80/(40x)/(20 + x)

⇒ (40 + 2x)/x hour

Now in this case,

A takes 1.5 hour more than B to travel 80 km

So,

⇒ (40 + 2x)/x - 80/x = 3/2

⇒ (40 + 2x - 80)/x = 3/2

⇒ 4x - 80 = 3x

⇒ x = 80

So,

Speed of B is 80 kmph.

Now,

To cover a distance of 120 km, B will take

⇒ 120/80 = 1.5 hours

∴ To cover a distance of 120 km, B will take 1.5 hours.