SOLUTION: Walking at 3/4 of her usual speed, Molly arrives at her destination 2.5 hours late. What is her usual time for walking this distance?

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Question 737833: Walking at 3/4 of her usual speed, Molly arrives at her destination 2.5 hours late. What is her usual time for walking this distance?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I will say that usually her motion equation is
(1) +d+=+r%2At+
When she walks at 3/4 her usual speed,
her equation is:
(2) +d+=+%283%2F4%29%2Ar%2A%28+t+%2B+2.5+%29+
--------------------------
The only units given are hours
I can say +d+=+1+ unit, miles or what ever, so
(1) +1+=+r%2At+
(2) +1+=+%283%2F4%29%2Ar%2A%28+t+%2B+2.5+%29+
--------------------------
(2) +1+=+%283%2F4%29%2A%28+r%2At+%2B+2.5r+%29+
Substitute (1) into (2)
(2) +1+=+%283%2F4%29%2A%28+1+%2B+2.5r+%29+
(2) +1+=+3%2F4+%2B+%283%2F4%29%2A%285%2F2%29%2Ar+
(2) +8+=+6+%2B+15r+
(2) +15r+=+2+
(2) +r+=+2%2F15+
and, since
(1) +1+=+r%2At+
(1) +1+=+%282%2F15%29%2At+
(1) +t+=+15%2F2+
(1) +t+=+7.5+
Her usual time is 7.5 hrs
check:
(2) +1+=+%283%2F4%29%2Ar%2A%28+t+%2B+2.5+%29+
(2) +1+=+%283%2F4%29%2A%282%2F15%29%2A%28+7.5+%2B+2.5+%29+
(2) +1+=+%286%2F60%29%2A10+
(2) +1+=+1+
Hope I got it