Word problem Linear

Question

LaTanya will walk her bike from her house to the bike shop, which is 1.5 mi from her house, to get the bike fixed. She expects to wait 30 minutes for the repair. The she will ride her bike home. Can she be home in one hour?

Answer 1

the time in minutes it will take her to walk her bike to the shop is 1.5/R*60 = 90/R, where R is her speed in miles per hour.

She will then have 30 - 90/R minutes to ride her bike back home.

In hours, this is (30-90/R)/60 = (1/2 - (3/2)/R)

Her speed riding her bike home is then 1.5 / (1/2 - (3/2)R)

For example, if her speed walking her bike to the shop is R=5 mph, then she will

get there in 90/5 = 18 minutes which is 18/60 = 9/30 = 3/10 hour.

She then has 12 minutes to ride her bike home, his is (1/2 - (3/2)/5) = (1/2 - 3/10) = 2/10 = 1/5 hour

Her return speed therefore is 1.5/ (1/5) = 5*1.5 = 7.5 mph

So as to keep these quantities positive, 30 - 90/R > 0 ---> 30 > 90/R ---> R > 90/30 =3, so

she MUST walk her bike at least 3 mph, and even then, she will have NO TIME to ride her

bike back.

4 mph means 90/4 = 22.5 minutes, which leaves 7.5 minutes to return.

1.5 / (7.5/60) = 1.5*60/7.5 = 75/7.5 = 10 mph on the return trip

So yes, it is possible but it will not be easy