Question : A car left 4 hours later than the scheduled time but in order to reach its destination 480 km away in time, it had to increase its usual speed by 10 km/hr. What is the usual speed of the car?
Option 1: 40 km/hr
Option 2: 60 km/hr
Option 3: 30 km/hr
Option 4: 50 km/hr

Question

Question : A man drives his car at a speed of 50 km/hr for 2 hours and then decides to slow down to 40 km/hr till the end of the journey. If his average speed for the journey was 44 km/hr, then for how much time did he drive his car at a speed of 40 km/hr?

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Answer 1

Correct Answer: 30 km/hr

Solution : Let the usual speed of the car as $v$ in km/hr.
The time it takes to travel 480 km at the usual speed is $\frac{480}{v}$ hours.
Because the car left 4 hours later than scheduled, it had to travel at a speed of $(v + 10)$ km/hr to reach its destination on time.
The time it takes to travel 480 km at this increased speed is $\frac{480}{(v + 10)}$ hours.
$\Rightarrow \frac{480}{v} = \frac{480}{(v + 10)} + 4$
$\Rightarrow v^{2} + 10 v - 1200 = 0$
$\Rightarrow (v + 40) (v - 30) = 0$
So, $v = 30$ , as speed cannot be negative.
Hence, the correct answer is 30 km/hr.

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Question : A car left 4 hours later than the scheduled time but in order to reach its destination 480 km away in time, it had to increase its usual speed by 10 km/hr. What is the usual speed of the car?Option 1: 40 km/hrOption 2: 60 km/hrOption 3: 30 km/hrOption 4: 50 km/hr

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Question : A car left 4 hours later than the scheduled time but in order to reach its destination 480 km away in time, it had to increase its usual speed by 10 km/hr. What is the usual speed of the car?
Option 1: 40 km/hr
Option 2: 60 km/hr
Option 3: 30 km/hr
Option 4: 50 km/hr