Need algebra help to solve a distance, rate and time problem using a system of linear equations

Algebra
Tutor: None Selected Time limit: 1 Day

Two cyclist leave towns 76 mi apart at the same time and travel towards each One cyclist travels 10mi/h slower than the other.  If the meet in 2 hours, what is the rate of each cyclist? 

Nov 15th, 2015

Thank you for the opportunity to help you with your question!

Let the speed of faster one be x mph and the speed of the other slower cyclist be y mph.

We have been given that the speed of one cyclist is 10 mph slower than the other.

Then the equation is ,x=y+10 ........eqn(1)

Also the distance traveled by cyclist of speed x mph =Speed*time ,d1 =2x,as the time taken is 2 hour.

Distance traveled by the cyclist of speed y mph ,d2=2y

As the two cyclist meet at some point after 2 hour therefore the sum of the distance must be equal to 76 mile

2x+2y+76

x+y=38 ...............eqn(2)

Solving both equation using substitution.Substitute x=y+10 in eqn(2),we get

y+10+y=38

2y=28

y=14 mph=>Speed of the slower cyclist(answer)

Speed of the faster cyclist=10+14=24 mph (answer)


Please rate my answer so that I can further help you in the future.Thanks
Nov 15th, 2015

Are you studying on the go? Check out our FREE app and post questions on the fly!
Download on the
App Store
...
Nov 15th, 2015
...
Nov 15th, 2015
Dec 2nd, 2016
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer