SOLUTION: A cyclist rode 40 mi. before having a flat tire and then walking 5 mi to a service station. The cycling rate was four times the walking rate. The time spent cycling and walking was

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Question 149371This question is from textbook Intermediate Algebra with Applications
: A cyclist rode 40 mi. before having a flat tire and then walking 5 mi to a service station. The cycling rate was four times the walking rate. The time spent cycling and walking was 5 h. Find the rate at which the cyclist was riding. This question is from textbook Intermediate Algebra with Applications

Found 2 solutions by ankor@dixie-net.com, mangopeeler07:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A cyclist rode 40 mi. before having a flat tire and then walking 5 mi to a service station. The cycling rate was four times the walking rate. The time spent cycling and walking was 5 h. Find the rate at which the cyclist was riding.
:
Let x = the walking rate
then
4x = the riding rate
:
Write a time equation: Time = distance%2Frate
:
Riding time + walking time = 5 hrs
40%2F4x + 5%2Fx = 5
Reduce the fraction:
10%2Fx + 5%2Fx = 5
15%2Fx = 5
Multiply both sides by x
5x = 15
x = 15%2F5
x = 3 mph is the walking rate
then
4(3) = 12 mph is the riding rate
;
:
Check solution
40%2F12 + 5%2F3 =
31%2F3 + 12%2F3 = 5 hrs

Answer by mangopeeler07(462) About Me  (Show Source):
You can put this solution on YOUR website!
A cyclist rode 40 mi. before having a flat tire and then walking 5 mi to a service station. The cycling rate was four times the walking rate. The time spent cycling and walking was 5 h. Find the rate at which the cyclist was riding.

total miles=45 miles
total time=5 hrs
walking speed=x mph
cycling speed=4x mph

40/4x+5/x=5-----------------------because miles over mph gives you hours

Common denominator=4x
40/4x+20/4x=5

Add the numerators
60/4x=5
Multiply both sides by 4x
60=20x

Divide by 20
3=x

walking speed=4 mph
cycling speed=12 mph