SOLUTION: B is due east of A. if they walk directly toward each other, they meet with each other after 2 hour.if they both walk east at constant speed, A will catch up to B after 10 hour. if

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Question 387898: B is due east of A. if they walk directly toward each other, they meet with each other after 2 hour.if they both walk east at constant speed, A will catch up to B after 10 hour. if they both walk west at constant speed, A will walk 30 km before B reaches A's home.
=>What is the distance between A and B's home?
=>What is each of their speed?
Answer by ankor@dixie-net.com(22740) (Show Source):
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B is due east of A. if they walk directly toward each other, they meet with each other after 2 hour.if they both walk east at constant speed, A will catch up to B after 10 hour. if they both walk west at constant speed, A will walk 30 km before B reaches A's home.
:
=>What is the distance between A and B's home?
Let d = distance from A to B
:
Let a = A's speed
Let b = B's speed
:
"if they walk directly toward each other, they meet with each other after 2 hour."
Write a distance equation from this statement:
d = 2a + 2b
:
"if they both walk east at constant speed, A will catch up to B after 10 hour."
Write a distance equation
10a - d = 10b
Replace d with (2a+2b)
10a -(2a+2b) = 10b
10a - 2a - 2b = 10b
10a - 2a = 10b + 2b
8a = 12b
Simplify, divide by 4
2a = 3b
a = 1.5b
:
"if they both walk west at constant speed, A will walk 30 km before B reaches A's home.
Write a time equation: Time = dist/speed
A's time = B's time
=
Replace a with 1.5b
=
Cancel 1.5 into 30
=
Multiply both sides by b
20 = d
d = 20 km is the distance between A & B
:
=>What is each of their speed?
:
2a + 2b = 20
Simplify divide by 2
a + b = 10
Replace a with 1.5b
1.5b + b = 10
2.5b = 10
b =
b = 4 km/hr is B's speed
then
a = 1.5(4) = 6 km/hr is A's speed