SOLUTION: Hi. My name is Allen and I'm having trouble with this word problem from my Calculus class. Thanks in advance. Car A and car B both travel 300 miles. Car A drove at an average s

Algebra ->  Equations -> SOLUTION: Hi. My name is Allen and I'm having trouble with this word problem from my Calculus class. Thanks in advance. Car A and car B both travel 300 miles. Car A drove at an average s      Log On


   

Question 712246: Hi. My name is Allen and I'm having trouble with this word problem from my Calculus class. Thanks in advance.
Car A and car B both travel 300 miles. Car A drove at an average speed of 10 miles per hour faster than car B and made the trip in one hour less time. Find the average speeds of both cars.
Car A = ________ mph
Car B = ________ mph
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Car A and car B both travel 300 miles.
Car A drove at an average speed of 10 miles per hour faster than car B and made the trip in one hour less time.
Find the average speeds of both cars.
-----
Car A DATA:
distance = 300 miles ; rate = x+10 mph ; time = d/r = 300/(x+10) hrs
-------------------------------
Car B DATA:
distance = 300 miles ; rate = x mph ; time = d/r = 300/x hrs
-----
Equation:
time B - time A = 1 hour
---
300/x - 300/(x+10) = 1
----
300x + 300*10 - 300x = x(x+10)
----
x^2 + 10x -3000 = 0
----
Factor:
(x+60)(x-50) = 0
x = 50 mph (Car B speed)
x+10 = 60 mph (Car A speed)
=============================
Cheers,
Stan H.
==================
Car A = ________ mph
Car B = ________ mph