When it was snowing, Kevin drove for 50 miles. When the snow stopped, he was able to drive 15 mph faster than he did while it was snowing. He drove for 30 miles after the snow stopped. If Kevin drove for a total of 1.5 hours, what was his speed while driving while it snowed?



Answer :

Answer:

  about 48.62 mph

Step-by-step explanation:

You want Kevin's speed while it was snowing if he drove 50 miles at that speed, then 30 more miles at a speed 15 mph faster. His total travel time was 1.5 hours.

Time

The relationship between time, speed and distance is ...

  t = d/s

If we let s represent Kevin's speed when it was snowing, then s+15 was his speed when it stopped. His total travel time is the sum of the times at the two speeds:

  1.5 = 50/s + 30/(s +15)

Solution

Multiplying by 2s(s+15), we get the quadratic equation ...

  3s² +45s = 100(s +15) +60s

  3s² -115s = 1500 . . . . . subtract 160s

  3(s -115/6)² = 1500 +3(115/6)²

  s -115/6 = √(31225/36) = (5/6)√1249

  s = (5/6)(23+√1249) ≈ 48.62 . . . . . . miles per hour

Kevin's speed while it snowed was about 48.62 mph.