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 (1.2m points)

Related questions

2 answers
asked Sep 10, 2021 in Word Problem Answers by LOlly | 1.3k views
1 answer
asked Oct 15, 2020 by okdoyn Level 1 User (660 points) | 492 views
1 answer
asked Oct 15, 2020 by okdoyn Level 1 User (660 points) | 317 views
1 answer
asked Oct 6, 2020 by okdoyn Level 1 User (660 points) | 519 views
1 answer
asked Sep 30, 2020 by okdoyn Level 1 User (660 points) | 362 views
1 answer
asked Jun 11, 2020 in Trigonometry Answers by okdoyn Level 1 User (660 points) | 469 views
1 answer
asked Jun 10, 2020 in Algebra 1 Answers by okdoyn Level 1 User (660 points) | 555 views
2 answers
asked Jun 9, 2020 in Trigonometry Answers by okdoyn Level 1 User (660 points) | 522 views
1 answer
asked Jun 9, 2020 in Trigonometry Answers by okdoyn Level 1 User (660 points) | 487 views
1 answer
asked Jun 9, 2020 in Algebra 1 Answers by okdoyn Level 1 User (660 points) | 422 views
1 answer
asked Jun 9, 2020 in Algebra 1 Answers by okdoyn Level 1 User (660 points) | 539 views
1 answer
asked Jan 28, 2020 by anonymous | 1.2k views
1 answer
asked Nov 25, 2019 by anonymous | 364 views
1 answer
asked Nov 25, 2019 by anonymous | 370 views
1 answer
asked Nov 25, 2019 by anonymous | 424 views
1 answer
asked Nov 25, 2019 by anonymous | 403 views
1 answer
asked Nov 25, 2019 by anonymous | 405 views
1 answer
asked Oct 8, 2019 by anonymous | 472 views
1 answer
asked Oct 2, 2019 by anonymous | 401 views
1 answer
asked Sep 28, 2019 by anonymous | 327 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!
87,516 questions
100,308 answers
2,420 comments
750,051 users