• Math

  Speed, Distance and Time (Class 8)

  Posted by Eshita Basak on June 23, 2023 at 8:51 pm

  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

  Punith replied 1 year, 3 months ago 2 Members · 1 Reply
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  Punith

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  June 23, 2023 at 10:30 pm

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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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