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sesenic [268]
2 years ago
14

A woman keeps fit by bicycling and running every day. Monday she spends hour at each activity, covering a total of 7 miles. On T

uesday, she runs for 17 minutes and cycles for 40 minutes, covering a total of 12.85 miles. Assuming her running and cycling speeds don't change from day to day, at what speed does she run and cycle?
Mathematics
1 answer:
Gekata [30.6K]2 years ago
3 0

Answer:

The speed does he run is 3 miles/hr and her cycling speed is 18 miles/hr.

Step-by-step explanation:

Consider the provided information.

Let x mi/h represents the rate of running and y mi/h represents the rate of  cycling.

Monday she spends 1/3 hour at each activity, covering a total of 7 miles.

\frac{1}{3}x+ \frac{1}{3}y=7

x+y=21

x=21-y

On Tuesday, she runs for 17 minutes and cycles for 40 minutes, covering a total of 12.85 miles.

Convert minutes to hours by dividing 60.

\frac{17}{60}x+ \frac{40}{60}y=12.85

17x+40y=771

Substitute x = 21-y in above equation,

17(21-y)+40y=771

357-17y+40y=771

23y=771-357

23y=414

y=18

Substitute the value of y in x=21-y

x=21-18

x=3

Hence, the speed does he run is 3 miles/hr and her cycling speed is 18 miles/hr.

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