A TRUCK leaves a truck stop at 9:00 a.m. and tavel toward Sturgis, Wyoming. At 10:00a.m. a motorcycle leaves the same truck stop and travels the same route. The motorcycle travels 15 mph faster than the truck by noon. the truck has traveled 20 miles further than the motorcycle. How fast is each vehicle?

Jazmin Booker

Jazmin Booker

Open question

2022-09-02

A TRUCK leaves a truck stop at 9:00 a.m. and tavel toward Sturgis, Wyoming. At 10:00a.m. a motorcycle leaves the same truck stop and travels the same route. The motorcycle travels 15 mph faster than the truck by noon. the truck has traveled 20 miles further than the motorcycle. How fast is each vehicle?

Answer & Explanation

Nezveda6q

Nezveda6q

Beginner2022-09-03Added 7 answers

use the equation distance equals rate times time
d=rt
then write an equation for each vehicle
so for the truck the distance is unknown so just put d
d=rt
then the rate is also unknown so put r
d=rt
for the time however you know it starts at 9:00 and and ends at 12:00 so t=3 hrs for the truck
d = r × 3
then write your second equation for the motorcycle so start with the general form
d=rt
then you know the truck is 20 miles further so the motorcycle is 20miles less then the truck so d m o t o r c y c l e = d 20
so the equation becomes
d-20=rt
then you know the speed is 15 mph more then the truck so r m o t o r c y c l e = r + 15
so the equation becomes
d-20=(r+15)t
for the time however you know it starts at 10:00 and and ends at12:00 so t=2 hrs for the motorcycle
so the equation becomes
d 20 = ( r + 15 ) × 2
so you get the equations
d = r × 3
d 20 = ( r + 15 ) × 2
then since you have d=r\times 3 just substitute d into the motorcycle equation so you can solve for r
( r × 3 ) 20 = ( r + 15 ) × 2
which becomes
3r-20=2(r+15)
then multiply r+15 by 2
3r-20=2r+30
then subtract 2r from each side
r-20=30
then add 20 to each side
r=50
so r_{truck}=50
but you still need to find r m o t o r c y c l e
so remember r m o t o r c y c l e = r + 15
so plug in 50 for r
r m o t o r c y c l e = 50 + 15
r m o t o r c y c l e = 65
Licinilg

Licinilg

Beginner2022-09-04Added 3 answers

The truck speed = x miles per hour
The Bike Speed = x + 15 miles per hour
The truck miles = 3 hours * x miles per hour
The bike miles = 2 hours * x + 15 miles per hour
The truck miles = the bike miles + 20 miles
3 hours * x miles per hour = [2 hours * x + 15 miles per hour] + 20miles
3 x 1 = 2 ( x + 15 ) 1 + 20
When we solve for x, we get x=50, so, the truck goes 50 miles perhour, the bike goes 65 miles per hour.

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