SOLUTION: i need help with this problem!! The ratio of Alex's cycling speed to Bart's cycling speed is 6:5. Bart leaves school at 3:00 pm and alex leaves at 3:10 pm. By 3:30, Alex is only 2

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Question 120599This question is from textbook algebra: structure and Method: book 1
: i need help with this problem!! The ratio of Alex's cycling speed to Bart's cycling speed is 6:5. Bart leaves school at 3:00 pm and alex leaves at 3:10 pm. By 3:30, Alex is only 2 km behind Bart. How fast is each boy going? PLEASE HELP!!! I AM SORRY IF THIS ISN'T ENOUGH INFO, BUT THAT IS ALL THAT IS IN THE BOOK!!!!!! This question is from textbook algebra: structure and Method: book 1

Found 2 solutions by scott8148, ankor@dixie-net.com:
Answer by scott8148(6628) (Show Source):
You can put this solution on YOUR website!
"The ratio of Alex's cycling speed to Bart's cycling speed is 6:5"
__ let 6x=Alex, so 5x=Bart

Bart travels for 1/2 hr (30 min) and Alex travels for 1/3 hr (20 min)
__ Bart goes 2 km farther
__ rate times time equals distance

6x(1/3)+2=5x(1/2) __ 2x+2=2.5 x __ 2=.5x

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
The ratio of Alex's cycling speed to Bart's cycling speed is 6:5. Bart leaves school at 3:00 pm and Alex leaves at 3:10 pm. By 3:30, Alex is only 2 km behind Bart. How fast is each boy going?
:
What we know here:
At 3:30:
B's traveling time = 30 min or hr
A's traveling time = 20 min or hr
:
If A's speed = x
Then B's speed = x
:
Write a distance equation: Distance = time * speed
:
B's dist - A's dist = 2 km
x - x = 2
:
x - x = 2
:
Multiply equation by 12 to get rid of the denominators
12*x - 12*x = 12(2)
:
Cancel out the denominators and you have:
:
5x - 4x = 24
x = 24 km/hr is A's speed
:
24 = 20 km/h is B's speed
:
:
Check their distances from the start at 3:30:
B travels *20 = 10 km
A travels *24 = 8 km; 2km difference as given