travel 92 miles, it takes Sue, 3 hours less time than it takes Doreen to travel 49 miles Sue travels 16 miles per hour faster than Doreen. Find times rates of b

Question

doreens mph and hour

sues mph and hour

Answer 1

V is Doreen's speed or VELOCITY

Then Sue's speed is V+16

It takes Doreen T hours to travel 49 miles

49 = T * v = Tv

92 = (T-3)* (V+16) = Tv + 16T - 3V - 48

92 = 49 + 16T - 3V - 48 <--- substitutes TV=49

92 = 16 T - 3V + 1

91 = 16 T - 3V

3v + 91 = 16 T

(3v + 91)/16 = t

substitutes this into 49 = T * v = Tv

49 = (3v+91)/16 * v

784 = (3v+91)v

0 = 3v^2 + 91v - 784

0 = (3v + 112)(v-7)

3v+112=0 results in negative measures

v-7=0 ---> v = 7

which forces t=7

Doreen travels 7 mph. She travels for 7 hours, for a distance of 49 miles.

Sue travels 23 mph for 4 hours, which is a distance if 92 miles.

Doreen 7 mph

Sue 23 mph