Question

Beth ran a 5 km race on Saturday. Tim ran a 4 mile race. Who ran farther?

- Please explain how you did it, thanks!

Answer 1

≈
12.14

m
p
h


Number of seconds to run the race is:

s
e
c
o
n
d
s
=
(
15

m
i
n
u
t
e
s
∗
60

s
e
c
o
n
d
s
m
i
n
u
t
e
)
+
23

s
e
c
o
n
d
s
=
923

s
e
c
o
n
d
s

The number of hours is:

h
o
u
r
s
=
923

s
e
c
o
n
d
s
∗
m
i
n
u
t
e
60

s
e
c
o
n
d
s
∗
h
o
u
r
60

m
i
n
u
t
e
s
≈
0.256

h
o
u
r
s

The number of kilometers per mile is
1.609
.

The number of miles in a 5-K race is:

m
i
l
e
s
=
5.0
k
m
∗
m
i
l
e
s
1.609

k
m
≈
3.107
m
i
l
e
s

The pace in miles per hour is:

m
p
h
=
3.107

m
i
l
e
s
0.256

h
o
u
r
s
≈
12.14

m
p
h
.

Answer 2

Answer: Tim

==========================================

Step-by-step explanation:

1 mile = 1.609 km approximately

This is something you either memorize or look up on a reference sheet.

Multiply both sides by 4 so that we determine how many kilometers are in 4 miles.

So,

1 mile = 1.609 km

4*(1 mile) = 4*(1.609 km)

4 miles = 6.436 km

Therefore, we can see that Beth ran 5 km and Tim ran approximately 6.436 km. Tim ran slightly farther.

---------

An alternative method is to convert 5 km to miles to find that 5 km = 3.107 miles approximately.

Compare Beth's amount (3.107 miles) to Tim's amount (4 miles) and we have extra proof Tim ran a bit longer distance.

---------

The key with either method is that we convert each measurement to the same unit. Both need to be km, or both need to be miles. This allows us to do a comparison to see which is bigger. Otherwise, it's like comparing apples to oranges.