word problem

Question

two buses leave a station at the same time and travel in opposite directions. one bus travels 10 mi/p/h faster than the other if the two buses are 312 mi apart  after 2 hours what is the rate of each bus

Answer 1

Abby,

 

Distance = rate * time or (rate)(time) or "rate multiplied by time"

 

Define these values for each of the buses.  Let's call them bus 1 and bus 2:

 

Bus 1:  distance traveled: x miles 

            rate: r miles/hour

            time: 2 hrs

 

Bus 2:  distance traveled: 312 miles - x miles

           rate: (r + 10) miles/hour

           time: 2 hours

 

Now, let's set up an equation for each bus:

 

Bus 1: x = (r)(2) or x = 2r

 

Bus 2: 312 - x = (r + 10)(2) or 312 - x = 2(r + 10)

 

We obtained a set of 2 equations:

 

1)  x = 2r

2)  312 - x = 2(r+10)

 

Substitute x in equation 2:

 

312 - 2r = 2(r + 10)

 

Expand and solve for r:

 

312 - 2r = 2r + 20

 

312 - 20 = 2r + 2r

 

292 = 4r

 

∴ r = 73  

 

This means that the speed of bus 1 is 73 miles/hour; and the speed of bus 2 is 83 miles/hour.

 

You may prove this answers by saying:

 

"At 73 miles/hr, bus 1 travels 146 miles in 2 hours; and

 at 83 miles/hr, bus 2 travels 166 miles in 2 hours. 

 The sum of the 2 distances is 312 miles"