SOLUTION: Sharon drove for part of a 150 km trop at 45 km/h and the rest of the trop at 75km/h. How far did she drive at each speed if the entire trip took her 2 hours 40 min? How do I set

Algebra ->  College  -> Linear Algebra -> SOLUTION: Sharon drove for part of a 150 km trop at 45 km/h and the rest of the trop at 75km/h. How far did she drive at each speed if the entire trip took her 2 hours 40 min? How do I set       Log On


   



Question 110959This question is from textbook Algebra and Trigonometry
: Sharon drove for part of a 150 km trop at 45 km/h and the rest of the trop at 75km/h. How far did she drive at each speed if the entire trip took her 2 hours 40 min?
How do I set up this problem?
This question is from textbook Algebra and Trigonometry

Found 2 solutions by scott8148, josmiceli:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
time=distance/rate ... let x="distance @ 45", so 150-x="distance @ 75" ... 2hr40min=2 2/3 = 8/3

(x/45)+((150-x)/75)=8/3

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
t%5Ba%5D+%2B+t%5Bb%5D+=+t
d%5Ba%5D%2Fr%5Ba%5D+%2B+d%5Bb%5D+%2Fr%5Bb%5D+=+t
d%5Bb%5D+=+150+-+d%5Ba%5D
I put all the times in minutes and rates in terms
of km/min. 2 hrs 40 min = 160 min
d%5Ba%5D+%2F+%2845%2F60%29+%2B+%28150+-+d%5Ba%5D%29+%2F+%2875%2F60%29+=+160
d%5Ba%5D+%2F+%283%2F4%29+%2B+%28150+-+d%5Ba%5D%29+%2F+%285%2F4%29+=+160
4%2Ad%5Ba%5D+%2F+3+%2B+4%2A%28150+-+d%5Ba%5D%29+%2F+5+=+160
5%2A4%2Ad%5Ba%5D+%2B+3%2A4%2A%28150+-+d%5Ba%5D%29+=+3%2A5%2A160
20%2Ad%5Ba%5D+%2B+1800+-+12%2Ad%5Ba%5D+=+2400
8%2Ad%5Ba%5D+=+600
d%5Ba%5D+=+75km answer
and
d%5Bb%5D+=+150+-+d%5Ba%5D
d%5Bb%5D+=+75km answer
She drove 75 km both parts of trip