Question

Stacy travels 4 mph less than 2 times as fast as Eric. Starting at the same point and traveling in the same direction, they are 222 miles apart after 6 hours. Find their speeds.

Answer 1

Stacy's speed is 78 mph and Eric's speed is 41 mph.

Step-by-step explanation

Let Stacy's speed be x.

Let Eric's speed be y.

Stacy travels 4 mph less than 2 times as fast as Eric. This means that:

x = 2y - 4 ____(1)

After 6 hours, they are 222 miles apart. This means that:

Stacy's distance = d miles

Eric's distance = (d - 222) miles

Speed is given as distance divided by time.

So, for Stacy, after 6 hours:

x = d / 6

=> d = 6x

and

For Eric:

y = (d - 222) / 6

Cross multiply:

6y = d - 222

d = 6y + 222

Equate the two d's:

6x = 6y + 222

=> 6x - 6y = 238 ___(2)

We now have two simultaneous equations:

x = 2y - 4 ____(1)

6x - 6y = 222 ___(2)

Put (1) in (2):

6(2y - 4) - 6y = 222

12y - 24 - 6y = 222

6y - 24 = 222

Collect like terms:

6y = 222 + 24

6y = 246

y = 246 / 6

y = 41 mph

Recall that:

x = 2y - 4

x = 2(41) - 4

x = 82 - 4

x = 78 mph

So, Stacy's speed is 78 mph and Eric's speed is 41 mph.