I have a question on my math quiz i had yesterday. I didn't know how to answer it. My teacher said to use 24 for how many hours he swam or something.

Question

A swimmer broke a world record by crossing the Atlantic ocean on a raft. He traveled about 44 miles each day by swimming s hours and floating f hours. The rates for swimming are 3 mph. The rates for floating are 1mph. Write a system of equations to represent this situation.

Answer 1

Hi Alex;

 

44 miles/day

s=3 miles/hour

f=1 miles/hour

The units are in hours and days.  All units must align before we may begin calculations.

(44 miles/day)[(1 day)/(24 hours)]

The unit of day is in the denominator and numerator.  It cancels...

(44 miles/day)[(1 day)/(24 hours)]

(44 miles/24 hours)

(11 miles/6 hours)

 

[(11 miles)/(6 hours)](total hours)=(3 miles/hour)(s hours)+(1 mile/hour)(f hours)

The units on both sides are (miles/hour)(hours).  These align.

Answer 2

Alex,

 

Your teacher hinted at 24 because that was the constraint for how many hours he spent swimming or floating to go 44 miles in a day.mso the first equation is:

S+f=24.

 

Since he swims at 1mph with the current he travels at 4mph swimming and floats with the current at 3mph making the second equation:

4s+3f=44.

 

Hope that helps,

Deanna