Question 1164012
Natasha rides her bike (at a constant speed) for 4 hours, helped by a 24) wind of 3 miles per hour. Pedaling at the same rate, the trip back against
the wind takes 10 hours. Find the total round trip distance she
traveled.
<pre>Let distance be D, and average speed, without the wind, be S
Then we get the following OUTGOING-SPEED equation: {{{system(matrix(1,3, D/4, "=", S + 3), matrix(1,6, D/4 - 3, "=", S, "----", eq, "(i)"))}}}
Also, the RETURN-SPEED equation is: {{{matrix(1,6, D/10, "=", S - 3, "------", eq, "(ii)")}}}
{{{matrix(1,3, D/10, "=", D/4 - 3 - 3)}}} ------ Substituting {{{D/4 - 3}}} for S in eq (ii)
{{{matrix(1,3, D/10, "=", D/4 - 6)}}}
2D = 5D - 120 ----- Multiplying by LCD, 20
2D - 5D = - 120
- 3D = - 120
Distance she traveled, one way, or {{{matrix(1,6, D, "=", (- 120)/(- 3), "=", 
40, miles)}}} 
Round-trip distance: {{{highlight_green(matrix(1,4, 2(40), "=", 80, miles))}}}.