SOLUTION: here is a math problem I need some help with Thanks. You are going on a one-way bus trip. You intend to ride the bus for a certain distance,get off,and walk back to your original

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Question 202435This question is from textbook Mathematics For Technical trades
: here is a math problem I need some help with Thanks.
You are going on a one-way bus trip. You intend to ride the bus for a certain distance,get off,and walk back to your original starting point taking the same route. If the bus travels at a rate of 9 miles per hour and you walk back at a rate of 3 miles per hour, how far would you ride so as to be back in 8 hours?
Use the formula:Distance=rate (times) time. This question is from textbook Mathematics For Technical trades

Found 2 solutions by rfer, jim_thompson5910:
Answer by rfer(16322) (Show Source):
You can put this solution on YOUR website!
d=rt
d=3(8)
d=24 mi

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Ignore the last solution. It is incorrect.

Start with the distance-rate-time equation

Plug in (the speed of the bus)

Divide both sides by 9 to isolate "t".

Rearrange the equation

So it takes the bus hours to go "d" miles.

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Go back to the distance-rate-time equation

Plug in (the walking speed)

Divide both sides by 3 to isolate "t".

Rearrange the equation

So you take hours to go "d" miles on foot.

Now add the two times and set them equal to 8:

The goal now is to solve for "d"

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Start with the given equation.

Multiply EVERY term by the LCD to clear any fractions.

Multiply and simplify.

Combine like terms on the left side.

Divide both sides by to isolate .

Reduce.

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Answer:

So the solution is

This means that you would ride the bus for 18 miles, get off, and then walk the 18 miles back.