SOLUTION: 1) A Commuter bus takes 2 hours to get downtown: an express bus, averaging 25mph faster, takes 45 minutes to cover the same route. What is the average speed for the commuter bus?

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: 1) A Commuter bus takes 2 hours to get downtown: an express bus, averaging 25mph faster, takes 45 minutes to cover the same route. What is the average speed for the commuter bus?       Log On

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Question 37851This question is from textbook
: 1) A Commuter bus takes 2 hours to get downtown: an express bus, averaging 25mph faster, takes 45 minutes to cover the same route. What is the average speed for the commuter bus?
Also...
2)You commute to work a distance of 40 miles and return on the same route at the end of the day. Your average rate on the return trip is 30 miles per hour faster that your average rate on the outgoing trip. If the round trip takes 2 hours, what is your average rate on the outgoing trip to work?

thank you so much!! This question is from textbook

Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
Let the x be the speed for computer bus
Let x+25 be the speed for express bus
2x=0.75(x+25)
2x=0.75x+18.75
1.25x=18.75
x=15
15+25=40
Hence a computer bus travels at 15mph and the express bus travels at 40mph.
2.

Let x be the speed.

On going = x

On returning = x+30

Equation:

40%2Fx%2B40%2F%28x%2B30%29=2

40[(x)+(x+30)]=2[(x)(x+30)]

40%282x%2B30%29=2%28x%5E2%2B30x%29

80x%2B1200=2x%5E2%2B60x

2x%5E2-20x-1200=0

x%5E2-10x-600=0

Solve the quadratic system and you get:

x=30

Hence, the speed of the car is 30mph.

Paul.