# Desiree drove north for 30 minutes at 50 miles per hour. Then, she drove south for 60 minutes at 20 miles per hour. How far and in what direction is Desiree from where she started?

Question
Ratios, rates, proportions
Desiree drove north for 30 minutes at 50 miles per hour. Then, she drove south for 60 minutes at 20 miles per hour. How far and in what direction is Desiree from where she started?

2020-10-24
# movement to north
- 1 hour = 60 min
- 50 miles ----------- 60 minutes ( = 1 hour )
Y miles ----------- 30 minutes
cross multiplying ( scissor )
60 Y = 50 x 30 = 1500 ( divide both sides over 60 )
$$\displaystyle{Y}=\frac{{1500}}{{60}}={25}$$ miles so, the distance she travels to north is 25 miles.
2 # movement to south ( opposite direction )
20 miles ------------- 60 minutes
Y miles ------------- 60 minutes
cross multiplying 60 Y = 20 x 60 = 1200 ( divide both sides over 60 )
Y = 1200 / 60 = 20 miles
but this distance is on the opposite direction to north ( south ) so it takes a ( - ) sign the distance she travels to south = - 20 miles
3the distance from where she started driving = the distance she travels to north + the distance she travels to south = 25 + ( - 20 ) = 5 miles 5 mile is ( + ) so the direction is to north

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