natasha rides her bike (at a constant speed) for 5 hours with help by a wind of 2 mph. pedaling at the same rate, the trip back against the wind takes 9 hours. Find the total roundtrip distance she traveled.

Question

kinggeorge · Answer

For this, you need to remember the equation distance=rate x time. 

When she was riding with the help of the wind, her rate was $r+2$ mph, where $r$ would be her rate in no wind. Against the wind, her rate would be $r-2$. We also know that the distance both with and against the wind was the same. So we have two equations.$$d=(r+2)*5$$$$d=(r-2)*9.$$Does this make sense so far?

anonymous · Answer

yes i have that down alread

anonymous · Answer

y

anonymous · Answer

i just dont know what to do next

kinggeorge · Answer

Next we set the two equations equal to each other.$$(r+2)*5=(r-2)*9\implies 5r+10=9r-18\implies28=4r\implies r=7.$$So the rate Natasha would go if there were no wind, is 7mph. Now we can just plug this value back into one of the original equations for $d$.$$d=(r+2)*5=(7+2)*5=9*5=45.$$Did this clear things up for you?

kinggeorge · Answer

However, you need to remember that this $d$ is just one way. So the roundtrip distance would be $2d=90$.

anonymous · Answer

Wow thank you so much. I appreciate it!

kinggeorge · Answer

You're very welcome.