Question : A vehicle is going at one-fourth of its usual speed and it takes an extra 45 minutes to reach its destination. It's usual time to cover the same distance is:
Option 1: 15 minutes
Option 2: 10 minutes
Option 3: 30 minutes
Option 4: 20 minutes
Correct Answer: 15 minutes
Solution :
Given,
A vehicle is going at one-fourth of its usual speed and it takes an extra 45 minutes to reach its destination.
We know that, time × Speed = Distance
Let the usual speed of the train and distance be 4S km/h and D km.
$\frac14$ of its usual speed = $\frac{4S}{4}$ = S km/h
Time to cover the distance = $\frac{D}{4S}$ hours
45 minutes = $\frac34$ hours
According to the question,
$\frac{D}{S}-\frac{D}{4S}=\frac34$
⇒ $\frac{4 - 1}{4S} = \frac{3}{4D}$
⇒ $\frac{3}{S} = \frac{3}{D}$
⇒ $\frac{D}{S} = 1$
⇒ $\frac{D}{4S}=\frac14$
= $\frac14$ hours
= $\frac14 × 60$
= 15 minutes
Hence, the correct answer is 15 minutes.
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