A swimmer can cross a lake in 15 minutes and 35 seconds while traveling at 3.85 miles per hour. If the swimmer wants to cross the lake in 13 minutes, how fast must he swim?

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Answer 1

Let's first start by identifying what we know (KNOWNS) and what we are being asked to find or the UNKNOWN.

KNOWNS:

Swimmer's speed = 3.85 miles/hour (Remember "per" is represented by an "/")

Time it takes for swimmer to cross lake = 15 min 35 sec

New time swimmer wants to cross lake in = 13 min

UNKNOWNS:

How fast must the swimmer travel to cross lake in new time (13 minutes)? Let's call this unknown "s" for speed.

SOLUTION:

1) Now in order to make the math easier, let's do a bit of unit analysis. What units are being used here for speed?

The swimmer's initial speed is 3.85 miles/hour or mph, so our final answer should also be in MILES PER HOUR. This means we are working with distance in the units of MILES and time in the units of HOURS.

We are given times in minutes and seconds, NOT HOURS. Let's change the times into the units we need or HOURS.

15 min and 35 sec needs to be converted to hours.

Convert each time into hours separately and add them together.

There are 60 min in an hour, so the conversion for minutes to hours is 60 min/hour.

There are 3,600 sec in an hour, so the conversion for seconds to hours is 3,600 sec/hour

15 minutes and 35 seconds

15 min => Divide 15 minutes by 60 min/hour or (15 min)/(60 min/hour) = 0.25 hours

Notice that the units to hour as follows (min/min/hour) = (min/min)/(1/hour) = 1/(1/hour) =

1 ÷ 1/hour = 1 x hour (when dividing by a fraction remember that we multiply by the reciprocal) = hour

35 sec => Divide 35 seconds by 3,600 sec/hour or (35 sec)/(3600 sec/hour) = 0.00972 hour

The units are cancelled the same way as in the minute conversion.

15 minutes and 35 seconds = 0.25 hours + 0.00972 hours = 0.25972 hours

13 minutes => Divide 13 minutes by 60 min/hour or (13 min)/(60 min/hour) = 0.217 hours

(See explanation in converting 15 minutes to hours for unit math)

2) Now we need a way to relate the two times. What stays the same in this question? Not the time the swimmer uses to cross the lake and not the speed at which the swimmer swims. The only thing that stays the same is the size of the lake. It will be the same no matter how fast the swimmer moves or how much time it takes for the swimmer to cross. (If we were working together, a picture would be REALLY useful here.)

To find out how long the lake is, we must use the speed at which the swimmer performed the first crossing or 3.85 miles per hour.

Miles per hour = Distance (d) divided by Time (t) = d/t = s (speed) We have mph = 3.85 miles/hour and time = 15 min and 35 seconds or 0.25972 hours (our conversion above.) This means we can solve for distance.

3.85 miles/hour = d/0.25972 hours Solve for d.

(3.85 miles/hour)(0.25972 hours) = (d/0.25972 hours)(0.25972 hours) = (d) (0.25972 hours/0.25972 hours) =

d x 1 = d

1 mile = d [Units: (miles/hour)(hours) = (miles/1)(hours/hours) = (miles/1)(1) = miles)]

Now we know that the swimmer wants to swim 1 mile in a new time of 13 minutes.

If s = d/t, and we know the lake's distance is 1 mile and we know the swimmer wants to swim that 1 mile in 13 minutes or 0.217 hours (from our conversion above), then using the equation we can calculate the swimmer's required speed in miles per hour.

s = (1 mile)/(0.271 hours) = 4.61 miles/hour or 4.61 mph

The swimmer must swim at least 4.61 miles per hour to cross the lake in at least 13 minutes.

Answer 2

r₁t₁ = r₂t₂

(38.5)(0.2597) = r₂(0.2167), convert minutes/seconds to hours

Can you calculate r₂ and answer?

Answer 3

First we should figure out the length of the lake:

15 min and 35 seconds = 0.25972 hours

3.85 mi/hr * 0.25972 hr = 1 mi

13 min = 13/60 = 0.2167 hours

1 mi /0.2167 hr = 4.62 mi/hr

He must travel ≥ 4.62 mi/hr