Darryl traveled to the lake and back. It took one hour longer to go there than it did to come back. The average speed on the trip there was 36 mph. The average speed on the way back was 45 mph. How many hours did the trip there take?

Question

anonymous · Answer

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We can state velocity as:
 $$V=\frac{  x}{  t}$$
So for the journey to the lake (t) and back (b) we can state:
 $$V_t=\frac{  x_t}{  t_t}$$ ,  $$V_b=\frac{  x_b}{  t_b}$$
Since:
$$ x_t =  x_b =x$$
Then:
$$V_t  t_t=V_b  t_b$$
From the drawing we can say:
$$(36)(t+1)=(45)(t)$$
$$36t+36=45t$$
$$45t-36t=36$$
$$9t=36$$
$$t=4$$
So for the journey to the lake we have:
$$t_t=t+1=5$$
And for the journey back we have:
$$t_b=t=4$$
But we want the total time, which is the sum of the time *to* and *back*:
$$t_{total}= t_t+t_b = 5+4=9$$