Question

In training for a triathlon, Yuna swam 1.9 miles in the open ocean, which took her 2 hours. For the first part of her swim, she averaged 1.4 miles per hour. For the second part of her swim, she swam against the current and started to tire, so her average speed decreased to 0.8 mph. What was the distance of the first part of Yuna's swim? Round to the nearest tenth as needed. The distance in the first part of her swim was miles.

Answer 1

The answer is 0.7 miles.

Answer 2

we know that

Yuna swam $1.9$miles in the open ocean in $2$ hours

so the average rate is equal to

$\frac{1.9}{2}=0.95\frac{miles}{hour}$

Let

x------> the distance in miles of the first part

y-----> the time in hours of the first part

we know that

First Part

$1.4=\frac{x}{y}$ -------> equation A

Second Part

$0.8=\frac{1.9-x}{2-y}$ -------> equation B

Using a graphing tool -----> to solve the system equations

see the attached figure

The solution is the point $(0.7,0.5)$

that means

$x=0.7\ miles\\y=0.5\ hours$

therefore

the answer is

The distance in the first part was $0.7\ miles$