Math question

Question

How many hours will a car traveling at 75 miles an hour take to catch up to a car traveling at 55 miles per hour if the slower car starts two hours before the faster car

Answer 1

The slower car has a 2 hour head start.

So at 55 mph it will have gone 110 miles.

 

The faster car goes 25 mph faster so it gains on the slow car at 25 mph.

In other words it gets 25 miles closer to the slow car every hour.

 

So just figure how long it takes to gain 110 miles at 25 mph.

 

Time = 110 miles              = ???

             25 miles / hour

 

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You could also solve it the way David W told you by making an equation

for how far each car traveled and setting them equal.

or 55 mph x t = 75 mph x (t-2)

then solve for t  - the answer either way is in hours.

Answer 2

Alright, Jussara, let's see what we can do.

 

Let's let t = the time of the first car (55 mph)

 

Then the time of the second car (75 mph) is t - 2, right?

 

Remember that distance travelled is rate x time.  When the cars meet, the distances will be the same, though our final answer is the value for t.

 

Is this enough information for you to do the problem?

Answer 3

The difference in speeds is 20mph rather than 25mph but if you use algebra you won't make this error.

 

If the faster car travels t hours when the faster car catches up, then the slower car traveled t + 2 hours because the slower car started 2 hours earlier.

 

If the car catches up, it means the two cars have traveled the same distance.

 

Distance  =  speed x time

Therefore set equal the distance traveled for each car

 

55(t + 2) = 75t

55t + 110 = 75t

110 = 20t

5.5 hours = t