Math word problems (Algebraic)

Question

Harry drove for 5 hours on the freeway then decreased his speed by 20 miles per hour and drove for 2 more hours on a country road. If his total trip was 373 miles, then what was his speed on the freeway?

Answer 1

D = r * t

373 = 7r

53.28 = average rate

 

Using the average rate, I'm going to test some respective zone speeds to see how close that mileage is to our true distance.

60 * 5 = 300

40 * 2 = 80

300 + 80 = 380, so it's very close; just 7 off. If we shave off one mph, we should get it (since we traveled for 7 hours).

 

59 * 5 = 295

39 * 2 = 78

295 + 78 = 373

Answer 2

Let, speed on freeway = x miles/hour

 

Distance covered in 5 hours on freeway = speed * time = x * 5 = 5x

 

Distance covered in 2 hours on the country road = speed * time = (x-20) * 2 = 2x - 40

Total distance covered: 5x + 2x - 40 = 373

 

7x -40 = 373

7x = 413

x = 59 miles/hour