# Vehicles Traveling In Opposite Directions

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#### mathdad

##### Full Member
A bus and a car leave the same place and traveled in opposite directions. If the bus is traveling at 50 mph and the car is traveling at 55 mph, in how many hours will they be 210 miles apart?

Solution:

Total distance = 210 miles

Bus rate = 50 mph
Bus time (in hours) = x

Car rate = 55 mph
Car time (in hours) = x

Set up:

50x + 55x = 210

Is this equation correct for vehicles traveling in opposite directions from the same starting point?

#### tkhunny

##### Moderator
Staff member
Looks good. Do you doubt?

#### mathdad

##### Full Member
Looks good. Do you doubt?
The word DOUBT walks with me in everything I do not just math.

#### Otis

##### Senior Member
... 50x + 55x = 210

Is this equation correct ...?
Yes. We can tell by thinking about the meaning. Draw a quick sketch or move two coins away from each other along a line, if you need help visualizing the scenario.

50x + 55x = 210

The first term is a distance (bus' rate × time)

The second term is a distance (car's rate × time)

Their sum is the total distance separating the vehicles after traveling x hours. • mathdad

#### mathdad

##### Full Member
Very good.

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