I need help

Question

Larry's time to travel 357 miles is 3 hours more than Terrell's time to travel 216 miles. Terrell drove 3 miles per hour faster than Larry. How fast did each one travel?

Answer 1

distance=rate*time

 

Larry

 

357=(r)(t+3) and (357)/(t+3)=r

 

Terrell

 

216=(r+3)(t)

substitute

216=([357/(t+3)]+3)t

multiply both sides by (t+3)

216(t+3)=(t+3)([357/(t+3)]+3)t

216(t+3)=(357+3(t+3))t

216t+648=357t+3t²+9t

3t²+357t+9t-216t-648=0

3t²+150-648=0

divide by 3

t²+50-216=0

216=2*2*2*3*3*3 and (2*2)(2*3*3*3)=4*54 and 54-4=50

(t+54)(t-4)=0

t-4=0

t=4

357=(r)(4+3)

357=(r)7

r=51 mph for Larry

216=(51+3)4

216=54*4

216=216

r=54 mph for Terrell

Answer 2

Larry is driving at 47 miles per hour since it takes him three (3) hours to travel 357 - 216 = 141 miles.

 

141 / 3 = 47, thus 47 miles per hour.

 

Since Terrell travels at 3 miles per hour faster than Larry, Terrell's speed of travel is equal to 47 + 3 = 50 miles per hour.

 

Larry = 47 miles per hour

Terrell = 50 miles per hour