Cars P & Q are approaching each other on the same highway. Car P is m

Hello Blackbox,

i also solved in same way as you did. But i took relative velocity 12 (61-49) as they move in opposite direction for 45 miles after they cross each other. but i did not get the correct answer.

Dear Blackbox & sunita123,

I'm happy to respond.

Blackbox, your approach was fine but was not the most efficient method. When the velocities are in opposite directions, we add the velocities, regardless of whether they are approaching head-on or receding in opposite directions. Thus, it is the same pattern for both distances in this problem, so we can just add the distances and divide by the sum of the speeds:
(120 + 45)/110 = 165/110 = 15*11/110 = 15/10 = 1.5 hr
That would be the most efficient method of solution.

sunita123, my friend, I'm sorry to say that you don't understand relative velocity. Once again, for relative velocity, you ADD if the velocities are in opposite direction and only SUBTRACT if the velocities are in the same direction. It's not a one-size-fits-all formula.

Does this make sense?
Mike

mikemcgarry - Thank you, kind sir! I have been watching Magoosh videos and have so far not regretted buying the product. It has proved to be very efficient with Rate problems. I did not know you could also combine the distances if two objects are traveling towards each other. I wish there were a video with such a example. But, of course, I understand there are only so many tutorial videos that could be showcased. Nevertheless, I am loving Magoosh Math! Thank you again.

For relative speed of bodies moving in opposite direction, the equation is (Sp + Sq) X t = Distance

Here, total distance need to be covered is 120+45=165 miles

So, the equation becomes \((49+61)t=165=>t=1.5\) hours

2:00 pm +1.5 hours=3:30 pm.

The answer is B
Total distance, which should be covered by both cars is 120+45=165 miles. Let x be the time so the equation will be 49x+61x=165 and x=1.5 hours

Car P is moving at 49 mph northbound and Car P is moving at 61 mph southbound


Shouldn't it be Car P and Car Q? :D

sunita123 - I wish I could help! This topic (when two objects travel at different speeds relative to each other) is confusing to me and I think Magoosh folks did a good job at explaining this- Add the two objects' individual speeds when they are traveling towards or away from each other. Subtract when they traveling along the same path). Therefore, I really don't know how to calculate with relative speed approach. Sorry!

Good one. I Didn’t realise I can just sum the distance.

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when you say for relative velocity, you ADD if the velocities are in opposite direction and only SUBTRACT if the velocities are in the same direction. It's not a one-size-fits-all formula. Can you please explain why we shouldn't subtract as they are travelling in opposite directions?

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