Question 1146049
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.