SOLUTION: Peter drove a distance of 189 miles. Part of the time he averaged 65 miles per hour and for the remaining time, 55 miles per hour. The entire trip tool 3 hours. How long did he tra

Question 236272: Peter drove a distance of 189 miles. Part of the time he averaged 65 miles per hour and for the remaining time, 55 miles per hour. The entire trip tool 3 hours. How long did he travel at each rate?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Peter drove a distance of 189 miles. Part of the time he averaged 65 miles per hour and for the remaining time, 55 miles per hour. The entire trip tool 3 hours. How long did he travel at each rate?
--------------------------------------------
1st part DATA:
distance = x miles ; rate = 65 mph ; time = d/r = x/65 hrs
-----------------------------
2nd part DATA:
distance = 189-x miles ; rate = 55 mph ; time = (189-x)/55 hrs.
---------------------------------
Equation:
1st time + 2nd time = 3 hrs
x/65 + (189-x)/55 = 3
55x + 65(189-x) = 3*55*65
55x + 65*189 - 65x = 165*65
-10x = -24*65
x = 156 miles (distance he traveled at 65 mph)
189-x = 33 miles (distance he traveled at 55 mph)
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Cheers,
Stan H.

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