Question

On a particular day, the wind added 4 miles per hour to Alfonso's rate when he was cycling with the wind and subtracted 4 miles per hour from his rate on his return trip. Alfonso found that in the same amount of time he could cycle 66 miles with the wind, he could go only 42 miles against the wind.What is his normal bicycling speed with no wind?

Answer 1

(v+4)t=66

t=66/(v+4)

...

(v-4)t=42, using t found above in this equation gives you:

66(v-4)/(v+4)=42 perform indicated multiplication on the left side

(66v-264)/(v+4)=42 multiply both sides by (v+4)

66v-264=42v+168 add 264 to both sides

66v=42v+432 subtract 42v from both sides

24v=432 divide both sides by 24

v=18

So his normal bicycling speed with no wind is 18 mph.