Question

Two cars simultaneously left Points A and B and headed towards each other, and met after 3 hours and 15 minutes. The distance between points A and B is 364 miles. What is the speeds of the cars, if one of the cars travels 12 mph faster than the other?

Answer 1

Answer:

Speed of one car=50 mph

Speed of another car=50+12=62 mph

Step-by-step explanation:

Speed of one  car= x mile/hr

Speed of another car=(x+12) miles/hr

Time=3 hours 15 minutes=$3+\frac{15}{60}=\frac{13}{4} hr$

Because 1 hr=60 minutes

Distance between point A and B=364 miles

Distance =$speed\times time$

According to question

$\frac{13}{4}x+\frac{13}{4}(x+12)=364$

$\frac{13x}{4}+\frac{13x}{4}+39=364$

$\frac{26x}{4}=364-39=325$

$\frac{13x}{2}=325$

$x=\frac{325\times 2}{13}=50$

Speed of one car=50 mph

Speed of another car=50+12=62 mph

Answer 2

Answer:

  50 mph, 62 mph

Step-by-step explanation:

Their total speed is found from ...

  speed = distance/time

  speed = (364 mi)/(3.25 h) = 112 mi/h

If s is the speed of the slower car, then ...

  s + (s+12) = 112 . . . . . their total speed is 112 mph

  2s = 100 . . . . . . . . . . simplify, subtract 12

  s = 50 . . . . . . . the speed of the slower car

  s+12 = 62 . . . . the speed of the faster car