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


You just need to think of the importance of this equation:  {{{RT = D}}}


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.