For a road trip a car of travelers can take the direct route or the scenic route. The scenic route takes 25% longer than the direct route. The group decides to take the direct route to their destination, and the scenic route on the return trip. If the total travel time to and from the destination is 12 hours, how long did the scenic route take

the scenic route take 6h 40m

Step-by-step explanation:

first we have to make an equation that represents the relationship of each route

x = scenic route

y = direct route

x = y + y * 25/100

now we have to make an equation that represents the routes over time

x + y = 12

we replace the x by what is the same in the first equation (y + y * 25/100) in the second equation

x + y = 12

(y + y * 25/100) + y = 12

2 y + 0.25 y = 12

2.25y = 12

y = 12/2.25

if we spend this in minutes multiplying it by 60

y = 12/2.25 * 60 = 320 m = 5h 20m

x + y = 12

x + (5h 20m) = 12h

x = 12h - 5h 20m

x = 6h 40m

the scenic route would take 6.67 hours.

Step-by-step explanation:

Let t represent the time it takes the team to travel through the direct route.

The scenic route takes 25% longer than the direct route. This means that the time it will take the team to travel through the scenic route is

t + (25/100 × t) = t + 0.25t = 1.25t

If the total travel time to and from the destination is 12 hours, it means that

t + 1.25t = 12

2.25t = 12

t = 12/2.25

t = 5.33 hours

The time it will take to travel the scenic route is

12/2.25 × 1.25 = 6.67 hours

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