Question 1146049: Tom leaves Los Angeles at 2:00 P.M. and drives to San Francisco, a distance of 268 miles, traveling east on highway 15 at 55 mph. At 2:15 P.M. Rob leaves San Francisco and drives to Los Angeles at 60 mph, traveling west on highway 15. At what time do they pass each other on the highway?
Found 3 solutions by Theo, Alan3354, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! rt=d
r = rate
t = time
d = distance
when they meet, tom will have been traveling for t hours and rob will have been traveling for t-.25 hours (15 minutes / 60 = 1/4 hours = .25 hours).
when they meet, the sum of the miles driven by tom and rob will be 268 miles.
the formula for tom is 55 * t = d1
the formula for rob is 60r * (t - .25) = d2
you have d1 + d2 = 268, so the formula becomes:
55 * t + 60 * (t-.25) = 268
simplify to get:
55 * t + 60 * t - 15 = 268
add 15 to both sides and combine like terms to get:
115 * t = 283
solve for t to get:
t = 283 /115 = 2.460869565
in t hours, tom has driven 55 * 2.460869565 = 135.3478261 miles
in t - .25 hours, rob has driven 60 * 2.210869565 = 132.6521739 miles.
the total miles driven is equal to 268 miles.
tom started at 2:00 pm.
in t hours, tom has driven 2 hours and 27.65217391 minutes.
that makes the time equal to 2.00 + 2:27.652173914 = 4:27.65217391 pm.
rob stated at 2:15 pm.
in t - .25 hours, tom has driven 2 hours and 12.65217391 minutes.
that makes the time equal to 2:15 + 2:12.65217391 = 4:27.65217391 pm
the time that they pass each other is at 4:27.65217391 pm.
round to the nearest minute and the time becomes 4:28 pm.
the conversion from hours to hours and minutes was done as follows:
2.460869565 hours * 60 = 147.6521739 minutes.
subtract 120 minutes and add 2 hours to get 2 hours 27.65217391 minutes.
that's the hours and minutes for tom.
rob traveled 15 minutes less, so rob traveled for 2 hours 12.65217391 minutes.
rob traveled 15 minutes less than tom.
the time they met was the same, as it should be.
Answer by Alan3354(69443)  (Show Source):
Answer by ikleyn(52776)  (Show Source):
You can put this solution on YOUR website! .
The cities names and all other input data (including highways, distance, "west" and "east") in this post are fictitious
and have no any relations to well known places and geographic notions.
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