SOLUTION: Traffic signals at each intersection on a main road all change on the same 2 minute cycle. A taxi driver knows that it is exactly 3.5km from one intersection to the next. Without b

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Question 1136050: Traffic signals at each intersection on a main road all change on the same 2 minute cycle. A taxi driver knows that it is exactly 3.5km from one intersection to the next. Without breaking the 50km/hr speed limit, what is the highest average speed, in kilometers per hour, he can travel to get to each intersection as it just changes to green?
Found 3 solutions by rothauserc, ikleyn, MathTherapy:
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
rate * time = distance
:
4/60 = 1/15 = 0.066666 is approximately 0.07 hour
:
If the car takes for 4 minutes between lights it will be in sync and
:
Note 2 minutes is too fast, 3.5/0.03 = 116.6667 km/hr
:
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rate = 3.5/0.07 = 50 km/hr
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:

Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
Moving 3.5 kilometers in 2 minutes, taxi driver has the speed  3.5%2F%28%282%2F60%29%29 = %283.5%2A60%29%2F2 = 3.5*30 = 105 km/h, 

which is an obvious violation of the 50 km/h speed limit.



Moving 3.5 kilometers in 4 minutes, taxi driver has the speed  3.5%2F%28%284%2F60%29%29 = %283.5%2A60%29%2F4 = 3.5*15 = 52.5 km/h, 

which is a violation of the 50 km/h speed limit, too.




Only moving 3.5 kilometers in 6 minutes, taxi driver reaches his goal without violation of the speed limit.

His speed in this case is  3.5%2F%28%286%2F60%29%29  %283.5%2A60%29%2F6 = 3.5*10 = 35 km/h.



ANSWER.  His safe highest speed is 35 kilometers per hour to reach his goal.


Ignore other answer by @rothauserc, since it is INCORRECT SOLUTION.


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Traffic signals at each intersection on a main road all change on the same 2 minute cycle. A taxi driver knows that it is exactly 3.5km from one intersection to the next. Without breaking the 50km/hr speed limit, what is the highest average speed, in kilometers per hour, he can travel to get to each intersection as it just changes to green?
Let the time it takes to get to each intersection be T

Then we get: matrix%284%2C1%2C+50+%3E+3.5%2FT%2C+50T+%3E+3.5%2C+T+%3E+3.5%2F50%2C+T+%3E+.07%29

.07 minutes = 

Therefore, T > 4.2 minutes

With T being > 4.2, and the light changing in INTERVALS of 2 minutes, then the time he needs to take to get to each GREEN light = 6 (2 * 3) minutes.

Travelling 3.5 km in 6 minutes, his speed MUST be: 

Tutor @IKLEYN is correct. The other person is WRONG!

Why don't they just leave these problems ALONE, and STOP leading these people ASTRAY? It's not helping when they provide WRONG, RIDICULOUS and/or NONSENSICAL answers.

He even got 2 minutes WRONG! FOR HIS INFORMATION, 2 minutes results in a speed of 105 km/h, EXACTLY, NOT 116+ km/h.