I need help with some questions

Question

Ian went to the coffee shop traveling 12 mph and returned home traveling 9 mph. If the total trip took 7 hours, how long did Ian travel at each speed?

Answer 1

This question is a worded system of equations.

The first sentence gives:

12x = 9y

[signifying x=time to go to the coffee shop & y=time to come back home. We know that the distance between the house and coffee shop doesn't change so distance = speed * time should be equal]

The second sentence gives:

x+y = 7

[signifying the total time taken was 7 hours]

Now solve for x and y using the two equations:

12x = 9y

x+y = 7

Note: there are multiple ways of solving this but I'll just modify the first equation to isolate x and then plug x into the second equation to find y

x = 9/12 y = 3/4 y [rewrite the first equation and plug into the second]

=> x+y = 7

3/4 y+y = 7

7/4 y = 7

y = 4

Plug it into one of the equations to find x:

12x = 9(4)

x = 36/12 = 3

x+(4) = 7

x = 7-4

x = 3

Ans: Ian traveled for 3 hours at 12 mph to go to the coffee shop and 4 hours at 9 mph to go home

Answer 2

t = d / r

(d / 12) + (d / 9) = 7

Dan you solve for d and answer?