`person(1)` traveled by `vehicle(1)` at an average speed of `SPEED1` miles per hour.

Then, `he(1)` traveled by `vehicle(2)` at an average speed of `SPEED2` miles per hour.

In total, `he(1)` traveled `DIST` miles for `plural(TIME, "hour")`.

How many miles did `person(1)` travel by `vehicle(1)`? (Round to the nearest mile.)

`round(DIST1)`

`d_`

miles`vehicleVar(1)` = `round(DIST1)`

How many miles did `person(1)` travel by `vehicle(2)`? (Round to the nearest mile.)

`round(DIST2)`

`d_`

miles`vehicleVar(2)` = `round(DIST2)`

How many minutes did `person(1)` travel by `vehicle(1)`? (Round to the nearest minute.)

`round(DIST1 / SPEED1 * 60)`

`t_`

minutes`vehicleVar(1)` = `round(DIST1 / SPEED1 * 60)`

How many minutes did `person(1)` travel by `vehicle(2)`? (Round to the nearest minute.)

`round(DIST2 / SPEED2 * 60)`

`t_`

minutes`vehicleVar(2)` = `round(DIST2 / SPEED2 * 60)`

Remember that `d = r * t`

, or written another way, `t = d / r`

.

`d_`

distance that `vehicleVar(1)` =`person(1)` traveled by `vehicle(1)`

`d_`

distance that `vehicleVar(2)` =`person(1)` traveled by `vehicle(2)`

Total distance: `d_`

`vehicleVar(1)` + d_`vehicleVar(2)` = `DIST`

Total time: `t_`

`vehicleVar(1)` + t_`vehicleVar(2)` = `TIME`

`t_`

and
`vehicleVar(1)` = (d_`vehicleVar(1)` / `SPEED1`)`t_`

`vehicleVar(2)` = (d_`vehicleVar(2)` / `SPEED2`)

Substitute the blue equations for:
`(d_`

`vehicleVar(1)` / `SPEED1`) + (d_`vehicleVar(2)` / `SPEED2`) = `TIME`

Multiply the above equation by `-1 * SPEED1`:
`-d_`

`vehicleVar(1)` - (`SPEED1` / `SPEED2`) * d_`vehicleVar(2)` = `-SPEED1 * TIME`

Add the two orange equations for:
`(`

`SPEED2 - SPEED1` / `SPEED2`) * d_`vehicleVar(2)` = `DIST - (SPEED1 * TIME)`

Calculating all variables (and then rounding to the nearest integer):

`d_`

`vehicleVar(2)` =`roundTo( 4 , DIST2 )` `(`

miles`round(DIST2)`)

`d_`

`vehicleVar(1)` =`roundTo( 4 , DIST1 )` `(`

miles`round(DIST1)`)

`t_`

`vehicleVar(1)` =`roundTo( 4 , DIST1 / SPEED1 * 60 )` `(`

minutes`round(DIST1 / SPEED1 * 60)`)

`t_`

`vehicleVar(2)` =`roundTo( 4 , DIST2 / SPEED2 * 60 )` `(`

minutes`round(DIST2 / SPEED2 * 60)`)