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
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
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
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 so the equation becomes d-20=rt then you know the speed is 15 mph more then the truck so 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
so you get the equations
then since you have d=r\times 3 just substitute d into the motorcycle equation so you can solve for r
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 so remember so plug in 50 for r
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
When we solve for x, we get x=50, so, the truck goes 50 miles perhour, the bike goes 65 miles per hour.