SOLUTION: Last weekend Oscar traveled by train to visit his grandparents. On Friday he boarded an express train that traveled at an average rate of 85 miles per hour. On Sunday he returned

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Question 937207: Last weekend Oscar traveled by train to visit his grandparents. On Friday he boarded an express train that traveled at an average rate of 85 miles per hour. On Sunday he returned home on a slower train that traveled at an average rate of 51 miles per hour. The total time Oscar spent on the trains last weekend was 8 hours. How many hours did Oscar spend on the train on Friday
Found 2 solutions by srinivas.g, stanbon:
Answer by srinivas.g(540) About Me  (Show Source):
You can put this solution on YOUR website!
let be x be the time spend on the train on Friday
ley y be the time spend on the train on sunday
total time spend on the trains = 8 hours
x+y =8 ..................eq(1)
let d be the distance from home to place of grand parents
during forward journey ,distance traveled = speed *time
=85*x
during return journey ,distance traveled = speed *time
=51*y
but in both journeys , distance traveled must be same
hence
85x =51y
move 51y to the left
85x-51y =0...................eq(2)
we need to eq(1), eq(2) to get x, y values
Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++1%5Cx+%2B+1%5Cy+=+8%2C%0D%0A++++85%5Cx+%2B+-51%5Cy+=+0+%29%0D%0A++We'll use substitution. After moving 1*y to the right, we get:
1%2Ax+=+8+-+1%2Ay, or x+=+8%2F1+-+1%2Ay%2F1. Substitute that
into another equation:
85%2A%288%2F1+-+1%2Ay%2F1%29+%2B+-51%5Cy+=+0 and simplify: So, we know that y=5. Since x+=+8%2F1+-+1%2Ay%2F1, x=3.

Answer: system%28+x=3%2C+y=5+%29.


hence time spend on the train on Friday = 3 hrs

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
On Friday he boarded an express train that traveled at an average rate of 85 miles per hour. On Sunday he returned home on a slower train that traveled at an average rate of 51 miles per hour. The total time Oscar spent on the trains last weekend was 8 hours. How many hours did Oscar spend on the train on Friday
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Friday DATA:
rate = 85 mph ; distance = x miles ; time = d/r = x/85 hrs
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Sunday DATA:
rate = 51 mph ; distance = x miles ; time = d/r = x/51
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Equation:
time + time = 8 hrs
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x/85 + x/51 = 8
51x + 85x = 8*85*51
136x = 8*85*51
x = 255 miles
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Friday time = x/85 = 255/85 = 3 hrs
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Cheers,
Stan H.
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