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3 years ago

To convert a capacity of 8.7 gallons to quarts, which ratio could you multiply by? remember that 1 gallon = 4 quarts.

Mathematics

1 answer:

Papessa [141]3 years ago

3 0

Using the factor label method, you would set up your ratio like so: $8.7 gall * \frac{4 qts}{1 gall}$

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3 years ago

a boat travels upstream on the allegheny river for 2 hours. the return trip only takes 1.7 hours because the boat travels 2.5 mi

Gre4nikov [31]

To solve this we are going to use the speed equation: $S= \frac{d}{t}$
where
$S$ is speed
$d$ is distance
$t$ time

We know from our problem that the upstream trip takes 2 hours, so $t_{u}=2$ . We also know that the downstream trip takes 1.7 hours, so $t_{d}=1.7$ . Notice that the distance of both trips is the same, so we are going to use $d$ to represent that distance.
Now, lets use our equation to relate the quantities:

For the upstream trip:
$S_{u}= \frac{d}{t_{u} }$
$S_{u}= \frac{d}{2}$ equation (1)

For the downstream trip:
$S_{d}= \frac{d}{t_{d} }$
$S_{d}= \frac{d}{1.7}$ equation (2)

We know that the boat travels 2.5 miles per hour faster downstream, so the speed of the boat upstream will be the speed of the boat downstream minus 2.5 miles per hour:
$S_{u}=S_{d}-2.5$ equation (3)

Replacing (3) in (1):
$S_{u}= \frac{d}{2}$
$S_{d}-2.5= \frac{d}{2}$ equation (4)

Solving for $d$ in equation (2):
$S_{d}= \frac{d}{1.7}$
$d=1.7S_{d}$ equation (5)

Replacing (5) in (4):
$S_{d}-2.5= \frac{d}{2}$
$S_{d}-2.5= \frac{1.7S_{d}}{2}$
$2(S_{d}-2.5)=1.7S_{d}$
$2S_{d}-5=1.7S_{d}$
$0.3S_{d}=5$
$S__{d}= \frac{5}{0.3}$
$S_{d}= \frac{50}{3}$ equation (6)

Replacing (6) in (5)
$d=1.7S_{d}$
$d=1.7( \frac{50}{3} )$
$d= \frac{85}{3}$ miles

We can conclude that the boat travel $\frac{85}{3}$ , which is approximately 28.3 miles, in one way.

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3 years ago