Michael drove to a friend’s house at a rate of 40 mi/h. He returned by the same route at a rate of 45 mi/h. The driving time for the round trip was 4 h. What is the total distance Michael traveled?

a.about 50 miles
b.about 169.4 miles
c.about 73 miles
d.about 201.6 miles

Question

Michael drove to a friend’s house at a rate of 40 mi/h.  He returned by the same route at a rate of 45 mi/h.  The driving time for the round trip was 4 h.  What is the total distance Michael traveled?

a.about 50 miles
b.about 169.4 miles
c.about 73 miles
d.about 201.6 miles

bahrom7893 · Answer

$$d=s*t$$$$d_1=s_1*t_1$$$$d_2=s_2*t_2$$$$d_1=d_2$$(since the route was the same), so we now know that: $$s_1*t_1=s_2*t_2$$$$40*t_1=45*t_2$$$$t_1=\frac{45*t_2}{40}=\frac{9*t_2}{8}$$

bahrom7893 · Answer

$$t_1+t_2=4$$$$t_2=4-t_1$$$$t_1=\frac{9*t_2}{8}=\frac{9*(4-t_1)}{8}=\frac{36-9t_1}{8}$$

bahrom7893 · Answer

$$8t_1=36-9t_1$$$$17t_1=36$$$$t_1\approx2.12h$$

bahrom7893 · Answer

$$d_1=s_1*t_1=40*2.12=84.8$$

bahrom7893 · Answer

$$d_2=d_1=84.8$$Total trip is:$$d_1+d_2=84.8+84.8=169.6$$

bahrom7893 · Answer

So, about 169.4 miles

anonymous · Answer

yep thanks