SOLUTION: An accountant rides a bus part of the way to work every day and walks the rest of the way. The bus averages 40 mph, and the accountant walks at a speed of 3 mph. The distance from

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Question 1101341: An accountant rides a bus part of the way to work every day and walks the rest of the way. The bus averages 40 mph, and the accountant walks at a speed of 3 mph. The distance from home to work is 17 miles, and the total time for the trip is 3 hours. Find how far the accountant walks and how far he rides the bus.
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
An accountant rides a bus part of the way to work every day and walks the rest of the way.
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The bus averages 40 mph, and the accountant walks at a speed of 3 mph. The distance from home to work is 17 miles, and the total time for the trip is 3 hours. Find how far the accountant walks and how far he rides the bus.
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40b + 3w = 17 miles
b + w = 3 hrs
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Modify::
40b + 3w = 17
3b + 3w = 9
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37b = 8
bus time = 8/37 hrs
distance the bus went = (8/37)40 = 8.65 miles
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40b + 3w = 17
40b + 40w = 120
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37w = 103
w = 103/37 hrs
Distance walked = (103/37)3 = 8.35 miles
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Cheers,
Stan H.
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Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = distance in miles traveled by bus
+17+-+d+ = distance in miles he walks
Let +t+ = time in hrs spent on bus
+3+-+t+ = time in hrs spent walking
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Equation for riding on bus:
(1) +d+=+40t+
Equation for walking:
(2) +17+-+d+=+3%2A%28+3+-+t+%29+
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(2) +17+-+d+=+9+-+3t+
(2) +d+=+3t+%2B+8+
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Set (1) = (2)
+40t+=+3t+%2B+8+
+37t+=+8+
+t+=+.2161+
and
+.2162%2A60+=+12.973+
+.973%2A60+=+58.4+
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+3+-+t+=+3+-+.2161+
+3+-+t+=+2.7839+
+.7839%2A60+=+47.0+
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He spent 12 min 58 sec on bus
He spent 2 hrs 47 min walking
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check:
+d+=+40t+
+d+=+40%2A.2161+
+d+=+8.644+ mi
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+17+-+d+=+3%2A%28+3+-+t+%29+
+17+-+d+=+3%2A2.7839+
+17+-+d+=+8.3517+
+d+=+17+-+8.3517+
+d+=+8.648+
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I think the error of +.004+ is due to
rounding off. check the math.