Question 73

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?

Solution

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 = 1.5zĀ  Ā  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.

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

=Ā $$\left(t-\frac{7}{10}\right)$$

Distance traveled by A =Ā Distance traveled by B

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

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

PutĀ 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 = $$2.1\times60$$Ā minutes

=Ā 126Ā minutes


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