# Rowan Boats went 4 miles upstream in the same amount of time h it took him to go 7 miles downstream. If the speed of the current is 3 mph, what was the speed of the rowboat?

tjbrewer | Certified Educator

` `The relationship between distance time and speed can be shown by using S for speed, d for distance and t for time.  `S=d/t ` If we use this formula for the rowing speed and apply it to the scenario of rowing upstream we get `(S-3)=4/h` We multiply each side by h and we get `h(S-3)=4`` `
Then we apply the same formula to the scenario going downstream and `S+3=7/h` Multiply by h and we get `h(S+3)=7` If we multiply each equation out we get
`Sh-3h=4` and
`Sh+3h=7` We add the two equations and we get `2Sh=11` We divide each side by 2h, and we get the speed expressed as `S=5.5/h` We then insert this value back into `Sh-3h=4` and we get `5.5/h xx h-3h=4` Which simplifies to `5.5-3h=4` Subtract 5.5 from each side `-3h=-1``.5` ` ` divide by -3 and `h=1/2`` ` hours.  Now we can substitute our value h into either equation and solve for S.

`S+3=7-:1/2`  This simplifies to `S+3=14` Subtract 3 from both sides and we get `S=11`mph.

or

`S-3=4-:1/2` This simplifies to `S-3=8`` ` Add 3 to each side and we get `S=11` mph

The rowing speed is 11 mph.