A motorist and cyclist starts from A to B at the same time where AB = 18km. The speed of motorist is 15kmph more than the cyclist. After covering half the distance the motorist rests for 30mins and there after his speed reduces by 20%. If the motorist reaches destination B 15min earlier than that of the cyclist. Then find the speed of the cyclist.
Answers
Answer:
12 km/h
Step-by-step explanation:
Let the motorist of the cyclist be x km/h
The speed of the cyclist is (x - 15) km/h
Find the reduced speed of the motorist:
Reduced speed = 80% of x = 0.8x
Time taken for the cyclist to reach the destination:
Time taken = Distance/Speed
Time taken = 18/(x-15) hour
Time taken for the motorist to reach the destination:
Time taken = Distance/Speed
Time taken for the first part of the journey = 9/x hour
Time taken to rest = 30 mins = 1/2 hour
Time taken for the second part of the journey =9 ÷ 0.8x = 45/4x
Time taken = 9/x + 1/2 + 45/4x
Time taken = 81/4x + 1/2
Solve x:
The cyclist needed 15 more time to reach the destination.
18/(x - 15) - (81/4x + 1/2) = 1/4
18/(x - 15) - 81/4x - 1/2 = 1/4
18/(x - 15) - 81/4x = 3/4
18(4x) - 81(x - 15) = 3/4 (4x)(x - 15)
72x - 81x + 1215 = 3x(x - 15)
-9x + 1215 = 3x² - 45x
3x² - 36x - 1215 = 0
x² - 12x - 405 = 0
(x - 27)(x + 15) = 0
x = 27 or x = -15 (rejected, speed cannot be negative)
Find the speed:
Cyclist = x - 15 = 27 - 15 = 12 km/h
Answer: The cyclist was traveling at 12 km/h