SOLUTION: anna and samantha are both going from boston to new york. Anna is going 20 mph faster than samantha. if it takes anna 3 hours to get to new york and samantha 4 hours, how fast is a

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Question 1127766: anna and samantha are both going from boston to new york. Anna is going 20 mph faster than samantha. if it takes anna 3 hours to get to new york and samantha 4 hours, how fast is anna going?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


There are many different ways to set up and solve this problem. I will show you a couple that I like best. Perhaps other tutors will respond showing different methods.

(1) Probably the usual algebraic method....

Let x be Samantha's speed
Then x+20 = Anna's speed

Anna drives for 3 hours to go the same distance Samantha goes in 4 hours:

3%28x%2B20%29+=+4%28x%29
3x%2B60+=+4x
60+=+x

Samantha's speed is x = 60 mph; Anna's is x+20 = 80 mph.

(2) The ratio of their times is 3:4, because Anna takes 3 hours and Samantha takes 4 hours. Since they are both driving the same distance, the ratio of their speeds is 4:3.

If the ratio of their speeds is 4:3 and Anna's speed is 20 mph faster, then the two speeds are 80 and 60 mph.