SOLUTION: please help with this problem: On a bicycle trip,Maria averaged 5 miles per hour faster for the first 60 miles than she did for the last 75 miles. The entire trip took 8 hours. F

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Question 43929This question is from textbook elementry and intermediate algebra
: please help with this problem:
On a bicycle trip,Maria averaged 5 miles per hour faster for the first 60 miles than she did for the last 75 miles. The entire trip took 8 hours. Find her rate for the first 60 miles. This question is from textbook elementry and intermediate algebra

Answer by adamchapman(301) About Me  (Show Source):
You can put this solution on YOUR website!
Write what we already know in equation form.
Let's use these symbols for our unknown variables:
x=rate for first 60 miles
y=rate for last 75 miles
We know from the question that x=y+5,
rearranging gives y=x-5
time = distance/speed
We know that the total time spent was 8 hours, so we can write:
8 = (60/x) + (75/y)
If we substitute y=x-5, we get:
8 = (60/x) + (75/(x-5))
multiplying both sides by (x-5):
8(x-5)=(60(x-5)/x)+75
multiplying both sides by (x):
8x(x-5)=60(x-5)+75x
rearranging:
8x^2-40x=60x-300+75x
8x^2-175x+300=0
using the quadratic solver: x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ;
x=1.875 or x=20
y is 5 less than x (y=x-5), and if x was 1.85, Maria would be cycling backwards for the second part of her journey!
Logic tells us that x must be 20 mph, implying that y=15mph
I hope this helps. If you have any other problems, please dont hesitate to contact me at adam.chapman@student.manchester.ac.uk