SOLUTION: A co-worker posed this problem this morning that his daughter had. I'm not sure enough information is given to arrive at a solution. A lady drives to her destination one day at

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Question 437871: A co-worker posed this problem this morning that his daughter had. I'm not sure enough information is given to arrive at a solution.
A lady drives to her destination one day at 40 mph.
Another day she drives at 56 mph.
She arrived at her destination the second day 2 hrs quicker than the first trip.
What was the distance of her trip?
Found 3 solutions by Alan3354, josmiceli, solver91311:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A lady drives to her destination one day at 40 mph.
Another day she drives at 56 mph.
She arrived at her destination the second day 2 hrs quicker than the first trip.
What was the distance of her trip?
-------------------
t = d/40
t-2 = d/56
(d/40) - 2 = d/56
56d - 2*2240 = 40d
16d = 4480
d = 280 miles

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The 1st day:
+d+=+r%2At+
+d+=+40t+
The 2nd day:
+d+=+56%2A%28t-2%29+
+d+=+56t+-+112+
------------
Since the distance are the same:
+40t+=+56t+-+112+
+16t+=+112+
+t+=+7+
and, since
+d+=+40t+
+d+=+40%2A7+
+d+=+280+
The distance was 280 mi
check answer:
+d+=+56%2A%28t-2%29+
+280+=+56%2A%287-2%29+
+280+=+56%2A5+
+280+=+280+
OK

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


You have all of the information you need.

Remember that distance equals rate times time, which is to say time is equal to distance divided by rate.

Let represent the distance we don't know but want to find and let represent the time. We are given the two rates, 40 and 56 mph.

The time taken for the first day's trip is then:



The time for the second day's trip is two hours less than the first day, so we can say:



Solve the second equation for in terms of everything else:



Simplify the RHS:



Now that we have two things both of which are equal to we can set them equal to each other.



Cross-multiply



Now all you have to do is distribute in the RHS, collect terms, and solve for

John

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