Travel distance

Question

Tom Quig traveled 300 miles east of St. Louis. For most of the trip he averaged 60 mph, but for one period of time he was slowed to 20 mph due to a major accident. If the total time of the travel was 7 hours, how many miles did he drive at the reduced speed?

Answer 1

Simple. Start with what you know. 

 

Total distance: 300 miles

Speeds: 60 mph &  20 mph

Total hours: 7 hours

 

Set the time spent doing 60 mph as x, and the time spend doing 20 mph as y. ()

 

60x + 20y = 300 miles      and       x + y = 7 hours

 

Solve for y first. 

 

x + y = 7 hours

y = 7 - x

 

Plug into the first equation for y. 

 

60x + 20(7 - x) = 300

 

Solve for x. 

 

60x + 140 - 20x = 300

40x +140 = 300

40x = 160

x = 4 hours

 

Then solve for y using the second equation. 

 

x + y = 7

 

(4) + y = 7

y = 3 hours

 

So, time spent doing 60 mph = 4 hours or 240 miles

and the time spend doing 20 mph = 3 hours or 60 miles

 

 

As always, go back and check!!!!!!!!

 

60x + 20y = 200 miles

 

 

60(4) + 20(3) = 300

240 + 60 = 300

300 = 300

 

 

 

Answer 2

Let x = miles driven at reduced speed

 

Then, 300-x = miles driven at full speed

 

Distance = (Rate)(Time), so Time = Distance/rate

 

Time at full speed + Time at reduced speed = 7

 

(300-x)/60 + x/20 = 7

 

Multiply by 60 to obtain:  300-x+3x = 420

 

                                             2x = 120

 

                                               x = 60 miles