Jamila left home on her bike at 11:00 AM traveling at 12 km/h. At noon, her sister Tamantha set out after her following the same route. If Tamantha's motorcycle traveled 28km/h, what time did Tamantha overtake Jamila?
Jamila went 12t km, (remember D=R*T)
Tamantha went 28(t-1) , she went 1 hour less than Jamila
But when she overtakes her sister, they went the same distance, so
28(t-1_ = 12t
28t - 12t = 28
16t=28
t = 1.75 which is 1 hour and 45 minutes
so Tamantha caught up with her sister 12:45 pm
Thank you!
To find out at what time Tamantha overtakes Jamila, we first need to determine the time it takes for Jamila to travel a certain distance.
We know that Jamila travels at a speed of 12 km/h. Let's consider the time it takes for her to be overtaken by Tamantha as 't' hours.
So, by the time Tamantha catches up to Jamila, Jamila would have been traveling for t hours at a speed of 12 km/h. This means that the distance traveled by Jamila is 12t km.
Now, we also know that Tamantha travels at a speed of 28 km/h. So, in the same 't' hours, Tamantha would have traveled a distance of 28t km.
Since they start at different times (Jamila at 11:00 AM and Tamantha at noon), the difference in their travel times is 1 hour (because noon is 1 hour after 11:00 AM).
Therefore, the equation representing this situation is:
12t + 12 = 28t
Now, we can solve for 't' to find the time it takes for Tamantha to overtake Jamila.
12t + 12 = 28t
12t - 28t = -12
-16t = -12
t = -12 / -16 = 0.75 hours = 45 minutes
So, Tamantha overtakes Jamila 45 minutes after she started her journey at 11:00 AM.
To find the exact time, we add 45 minutes to the starting time:
11:00 AM + 45 minutes = 11:45 AM
Therefore, Tamantha overtakes Jamila at 11:45 AM.