A person can walk 1 mile in 25 minutes. At the same rate how long would it take the person to walk 5 kilometers if 1 mile= 1.61 kilometers?

Question

Hi! Please explain! Thank you!

Answer 1

 

This is a D-I-R-T (Distance-Is-Rate-times-Time) problem.  The formula is:  D=RT.  To answer the question, we solve the equation for T:

  T=D/R

The problem gives:

  D= 5 km

  R = (1 mile) / (25 minutes)

So,

  T = (5 km) / ( (1 mile)/(25 minutes))

  T = (5 km) * (25 minutes) / (1 mile)         [invert denominator and multiply]

  T = (5 km)*(25 min) / (1.61 km)               [1 mile = 1.61 km]

In order to change units without changing a value, we will multiply by the multiplicative identity (that is, 1).
     [note: we can multiply 1 mi * (1.61 km / mi) = 1.61 km; or we just substitute for 1 mi)

  T = (5)(25)/1.61  min     [note km cancels out, leaving only min]

  T = 77.6 minutes

  T = 1 hour 18 minutes     [rounded to minutes, since that’s what problem gave us]

Answer 2

Hi Lynn,

 

Let's begin by converting 1 mile into its equivalent km using our given conversion ratio:

    (1 mile)(1.61 km / 1 mile) = 1.61 km

 

Next, let's set up this proportion (equivalent ratios) to

determine our unknown time (x):

    km : minutes = km : minutes

    1.61 : 25 = 5 : x

 

Next, let's solve this proportion for our unknown time (x):

    1.61 : 25 = 5 : x

    1.61/25 = 5/x

    (1.61)(x) = (25)(5)  

        [cross products of a proportion are equal]

    1.61x = 125

    x = 125/1.61

    x = 77 and 103/161

    x = 78 minutes (rounded up to nearest minute)

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.

Answer 3

OK, I think the conversion is what's making it confusing, so let's clear that out of the way first!

 

You know that 1 mi took 25 min to walk and you also know that 1 mi equals 1.61 km. So instead of saying 1 mi, say 1.61 km because they're equal (it's much like saying "I watched T.V. for 60 min" instead of "I watched T.V. for 1 hr"...it's just worded differently).

 

Now the relationship is: 1.61km in 25 min. However, you were asked how long would it take to walk 5 km. So we can set up a proportion.

 

Here is how you would set it up: you would have both the numerator and denominator having the same unit while the fraction represents one object.

For this proposed problem I would set up one of the fractions for the given walking rate. The numerator would have the km over time as the denominator. The other fraction would have the 5 km over the unknown time it would take. This makes it so the numerators have the same unit (distance in km) while the denominators also share a unit (time in min).

Here are the fractions with the numbers in place: 1.61km/25 min = 5km/x min. So now to solve for x, you cross multiply. This is done by making a zigzag pattern with the math by multiplying diagonally first before dividing the numbers so you would end up at the spot where x would be. So here, you would multiply 5 by 25 (which is 125) and then divide by 1.61. The answer here when rounded would be 77.64 min (125÷1.61≈77.64 min).

 

This should make sense: 1.61 is roughly a third of 5 so if the distance was three times as much, then the time should be 3 times greater than before.