SOLUTION: A bus leaves Denver at 9:00 a.m. and heads towards Kansas City, 600 miles away. At the same time, a train leaves Kansas City and heads for Denver at 80 mph. If the vehicles meet at

Question 1207249: A bus leaves Denver at 9:00 a.m. and heads towards Kansas City, 600 miles away. At the same time, a train leaves Kansas City and heads for Denver at 80 mph. If the vehicles meet at 1 pm, how fast was the bus traveling?
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website!
.

Denver, Colorado is in other time zone: it is 1 hour behind Kansas City, Missouri.

Therefore, wording expressions like " . . . at the same time . . . " are ambiguous and require clarifications.

Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Answer: 70 mph

Explanation

The time gap from 9:00 AM to 1:00 PM is 4 hours.
Think of it like 9:00 AM to 12:00 PM noon (3 hours) and then 12:00 PM noon to 1:00 PM is an extra hour (3+1 = 4 hours total).
Or think of 1:00 PM as 1300 in military time aka 24 hour time format.
9:00 AM would be 0900.
1300-0900 = 400 ---> 4 hours

The train goes from Kansas City to Denver at 80 mph and travels 4 hours when the train passes the bus.
The train has traveled 80*4 = 320 miles at this point.
Formula: distance = rate*time

x = speed of the bus in mph

The train has already covered 320 miles of the 600 mile total distance.
That leaves the remaining 600-320 = 280 miles for the bus to cover.
distance = rate*time
280 = x*4
x = 280/4
x = 70 mph is the speed of the bus.

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