SOLUTION: On a 5 hour trip, Thomas drove part of the time at 30mph and the rest at 55mph. If he traveled a distance of 250mi, how much time did he spend driving at 55 mph?
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Question 255101: On a 5 hour trip, Thomas drove part of the time at 30mph and the rest at 55mph. If he traveled a distance of 250mi, how much time did he spend driving at 55 mph?
This a one of the questions i am trying to solve to prepare for my midterm. If you could help explain to me step by step how to do this that would be great.
Thankyou Answer by richwmiller(17219) (Show Source):
You can put this solution on YOUR website! first we must know the formula for distance in terms of speed and time
rt=d
we will consider this little trip as two different trips taken one after another with a total time of 5 hours and a total distance of 250 miles.
rt+rt=d
We know the total time was 5 hours and the parts add up to 5
So let t = the second part and 5-t the first part
[We could also have said s for first part and t for second part
t+s=5
then we would have to solve for s in terms of t
s=5-t does that look familiar?
and substitute. But the first method is a shortcut.]
30*(5-t)+55*(t)=250
So just multiply it out and solve for t
t will be the time at 55 mph
[If we wanted to solve for just the 30 mph part we would have set t for it and 5-t for the 55 ]
30*(5-t)+55*(t)=250
150-30t+55t=250
subtract 150 from both sides
add 55t-30t
then you will have to divide that to get t alone on one side
