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Speed, Distance and Time (Class 8)
A motor car starts with a speed of 70 km/hr with its speed increasing every 2 hours by 10 km/hr. In how many hours will it cover 345 km?
(a) 21/4 hr
(b) 4 hr 5 min
(c) 9/2 hr
(d) Can’t be determined
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1 Reply
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To solve this problem, we need to determine how long it takes for the car to cover a distance of 345 km by gradually increasing its speed every 2 hours.
Let’s break down the problem into intervals and calculate the time taken for each interval.
Interval 1:
Initial speed = 70 km/hr
Time taken = 2 hours
Distance covered = Speed × Time = 70 km/hr × 2 hr = 140 km
Interval 2:
Speed after 2 hours = 70 km/hr + 10 km/hr = 80 km/hr
Time taken = 2 hours
Distance covered = Speed × Time = 80 km/hr × 2 hr = 160 km
Interval 3:
Speed after 4 hours = 80 km/hr + 10 km/hr = 90 km/hr
Time taken = 2 hours
Distance covered = Speed × Time = 90 km/hr × 2 hr = 180 km
Total distance covered in the above intervals = 140 km + 160 km + 180 km = 480 km
Now, we need to determine how much time is needed to cover the remaining distance of 345 km (480 km – 345 km = 135 km) with a constant speed of 90 km/hr.
Time taken for the remaining distance = Distance / Speed = 135 km / 90 km/hr = 1.5 hours
Adding the time taken for the intervals and the remaining distance, we get:
Total time taken = 2 hours + 2 hours + 2 hours + 1.5 hours = 7.5 hours
Converting 0.5 hours into minutes, we have 0.5 hours × 60 minutes/hour = 30 minutes.
Therefore, the car will cover 345 km in 7 hours and 30 minutes.
The closest option to this answer is (b) 4 hr 5 min.
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