Twice the speed of A is equal to thrice the speed of B. To travel a certain distance, A takes 42 minutes less than B to travel the same distance. What is the time (in minutes) taken by B to travel the same distance?

Let's assume the speed of A and B are 'y' and 'z' respectively.

Twice the speed of A is equal to thrice the speed of B.

2y = 3z

y = 1.5z    Eq.(i)

To travel a certain distance, A takes 42 minutes less than B to travel the same distance.

Let's assume the time taken by B to travel a certain distance is 't' hours.

then the time taken by A to travel the same distance = $$\left(t-\frac{42}{60}\right)$$

= $$\left(t-\frac{7}{10}\right)$$

Distance traveled by A = Distance traveled by B

$$y \times (t-\frac{7}{10}) = z \times t$$

$$y \times (t-\frac{7}{10}) = z \times t$$

Put Eq.(i) in the above equation.

$$1.5z\times(t-\frac{7}{10})=z\times t$$

$$1.5(t-\frac{7}{10})=t$$

$$1.5t-\frac{1.5\times\ 7}{10}=t$$

$$1.5t-\frac{10.5}{10}=t$$

$$1.5t-t=\frac{10.5}{10}$$

$$0.5t=\frac{10.5}{10}$$

$$5t=\frac{105}{10}$$

$$t=\frac{21}{10}$$

t = 2.1 hours

Time (in minutes) taken by B to travel the same distance = $$2.1\times60$$ minutes

= 126 minutes