SOLUTION: A driver travels 12 miles to work at a constant speed and travels the same distance home also at a constant speed. His speed on the trip home is 10 miles per hour faster than the t

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Question 262716: A driver travels 12 miles to work at a constant speed and travels the same distance home also at a constant speed. His speed on the trip home is 10 miles per hour faster than the trip to work and the total time for both trips is 1 hours. Find his speed on the way to work.
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
This is an RTD problem. Here is a table based on the given information:
Driver . . . . . . . .rate . . . . . . . . time . . . . . . . .distance
work. . . . . . . . . R. . . . . . . . . . . .T. . . . . . . . . . . .12 . .
home. . . . . . . . .R+10 . . . . . . . . 1-T. . . . . . . .. 12. . .
totals. . . . . . . . . . . . . . . . . . . . .1 . . . . . . . . . . . . . .
we have the equation
rt = d
solve this for t and we get
t = d/r
From above,
T+=+12%2FR
and
1-T+=+12%2F%28R%2B10%29
So,
T+=+1+-+12%2F%28R%2B10%29
The sum of the times = 1 hr, so
12%2FR+%2B+1-+%281+-+12%2F%28R%2B10%29%29+=+1
step 1 - multiply by the common denominator of R(R+10) to get
12%28R%2B10%29+%2B+R%28R%2B10%29+-R%28R%2B10%29+%2B+12R+=+R%28R%2B10%29
step 2 - distribute to get
12R+%2B+120+%2BR%5E2+%2B+10R+-R%5E2+-10R+%2B+12R+=+R%5E2+%2B+10R
step 3 - combine like terms on the left to get
24R+%2B+120+=+R%5E2+%2B+10R
step 4- setting = 0, we get
R%5E2+-14R+-+120+=+0
step 5 - factoring, we get
%28R-20%29%28R%2B7%29+=+0
step 6 - solved for R we get
R = 20
or
R = -7
--
So, R = 20 mpg on the way to work