Allen, Benedict and Carl started at the same instant from the same point using the same route trying to overtake a fourth cyclist Donald traveling at a constant speed ahead of them. Allen and Benedict each took 10 hours and 4 hours respectively to overtake Donald. Given that Allen, Benedict and Carl each cycled at the constane speed of 4 km/h, 5.5 km/h and 7 km/h respectively throughout the journey, find the time, in hours, that Carl took to overtake Donald.
by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

A=4t represents the distance (km) Allen travels in time t.

B=5.5t similarly represents the distance Benedict travels.

C=7t represents how far Carl travels.

D=dt+h represents how far Donald travels, where d is Donald’s speed in km/hr and h is the headway Donald has because he leaves before the other cyclists.

When t=10 hr, A=4×10=40km, and D=10d+h.

When t=4 hr, B=4×5.5=22km, and D=4d+h.

Therefore we have:

10d+h=40 because A=D when Allen overtakes Donald.

4d+h=22 because B=D when Benedict overtakes Donald.

Subtracting these two equations we get:

6d=18, so d=3km/hr, Donald’s speed.

And h=22-4d=40-10d=10km, the headway at the start.

So D=3t+10. C=7t, so when C=D, 7t=3t+10, 4t=10, t=2.5hr, the time it takes Carl to overtake Donald.

by Top Rated User (711k points)

Related questions

1 answer
asked Nov 25 by anonymous | 67 views
1 answer
asked Nov 25 by anonymous | 47 views
1 answer
asked Nov 25 by anonymous | 49 views
1 answer
asked Nov 25 by anonymous | 43 views
1 answer
asked Nov 25 by anonymous | 45 views
1 answer
asked Oct 8 by anonymous | 37 views
1 answer
asked Oct 2 by anonymous | 49 views
1 answer
asked Sep 28 by anonymous | 41 views
1 answer
asked Sep 28 by anonymous | 54 views
1 answer
asked Sep 18 by anonymous | 38 views
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
84,412 questions
89,225 answers
1,990 comments
7,511 users