SOLUTION: Juan left home on his bicycle at 10:00 a.m. traveling at 21 km/h. At noon, his brother set out after him on his motorcycle following the same route. If the motorcycle traveled at 6

Question 286464: Juan left home on his bicycle at 10:00 a.m. traveling at 21 km/h. At noon, his brother set out after him on his motorcycle following the same route. If the motorcycle traveled at 63 km/h, what time did Juan's brother overtake him?
Thank you, sir
Found 2 solutions by texttutoring, PRMath:
Answer by texttutoring(324) (Show Source): You can put this solution on YOUR website!
Let Vb=velocity of the bike=21km/h
Vm=velocity of the motorcycle = 63km/h
The distances they travel are equal, because it's the same route and they left from the same place. We know the equation D=VT, where D=distance, V=velocity and T=time. Because the distances for the motorcycle and bike are the same, we can just set them equal to each other:
D=D
Vb*Tb = Vm*Tm
The time the motorcycle travels is 2 hours less than the time the bike travels, so Tm=Tb-2
Vb*Tb = Vm(Tm-2)
21Tb = 63(Tb-2)
126 = 42Tb
Tb=3
The bike travels for 3 hours. The motorcycle travels for 2 hours less, so 1 hour. They meet at 1:00pm.
Answer by PRMath(133) (Show Source): You can put this solution on YOUR website!
Juan left home on his bicycle at 10:00 a.m. traveling at 21 km/h. At noon, his brother set out after him on his motorcycle following the same route. If the motorcycle traveled at 63 km/h, what time did Juan's brother overtake him?
Thank you, sir

You just need to think of the importance of this equation:

In other words, RATE times TIME equals DISTANCE.

Now....with that info, make a little chart for yourself:

________RATE_______TIME______DISTANCE_________
Juan..............21.........................T............................D............
Brother........63.........................T -2......................D............

See, the brother started out two hours behind Juan, or T - 2.

Also, when the brother overtakes Juan, then that means they will be at the exact same place, or the exact distance from the starting point. In other words: The distance for Juan equals the distance for the Brother.

Knowing that they have to be at the same distance means that you set up an
equation of: Distance = Distance (Or D = D)

SO... let's say:
D = D What does "D" equal?

"D" equals RATE times TIME.
For Juan, the RATE times TIME is: 21(T).
For the brother the RATE times TIME is 63(T - 2)

Let's fill in that info:

D = D
21(T) = 63(T - 2) Now let's distribute the 63 to the T and 63 to the -2.
21T = 63T - 126 Now let's subtract 63T from both sides to get the T variables on one side.
21T - 63T = -126 Now let's subtract: 21T - 63T which is: -42T
-42T = -126 Now divide both sides by -42 to further isolate the T.
T = 3

Now if T equals 3 hours, let's see how that works:

Juan is traveling 21 kmp. In three hours that's:
21(T) which is
21(3) = 63 Kilometers.

The brother is traveling 63 kmp. In T - 2 hours that's:
T - 2 which is 3 -2 = 1
63(1) = 63 Kilometers.

SOoo in 1 hour, the brother will be at the 63 kilometer mark. Since the brother took off at noon, in 1 hour it will be 1 pm. It will also be 1 pm for Juan if he travels for 3 hours from 10 a.m.

I hope this helps you. And a "sir" did not answer your question. :-) A girl did. :-) Sometimes math types are girls, too.
Good luck with your math.
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