Algebra 2 Question, Please Help

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

Let x = Alphonso's normal cycling speed

 

     distance = speed*time

     distance/speed = time

 

With the wind, speed = x + 4. Against the wind, speed = x - 4

 

     66/(x+4) = time

     42/(x-4) = time

 

Since the times are equal:

 

     66/(x+4) = 42/(x-4)

     66(x-4) = 42(x+4)

     66x - 264 = 42x + 168

     24x = 432

     x = 18 mph

Answer 2

a = alfonso's speed with no wind

 

the wind added 4 mph to alfonso's rate (when he was cycling with the wind)

a+4 = rate with wind

 

and subtracted 4 miles per hour from his rate on his return trip.

a-4 = rate against wind

 

alfonso found that in the same amount of time he could cycle 66 miles with the wind,

 

66 = distance with wind

t = same time for both trips

 

he could go only 42 miles against the wind.

42 = distance against wind

 

what is his normal bicycling speed with no wind

find a 

 

solution:

distance = rate × time 

with wind: 66 = (a+4)(t)

against wind: 42 = (a-4)(t)

 

solve both for t:

with wind: 66/(a+4) = t

against wind: 42/(a-4) = t

 

since t is same for both, set expressions equal:

66/(a+4) = 42/(a-4)       cross multiply

66(a-4) = 42(a+4)          distribute

66a - 264 = 42a + 168       add 264 to  and subtract 42a from both sides

24a = 432    divide both sides by 24

a = 18

 

Alfonso's normal bicycling speed is 18 mph with no wind.

 

check:

66/(18+4) = 66/22 = 3 hours

42/(18-4) = 42/16 = 3 hours