BB leaves at 70 mph; PH leaves at 100 mph 30 mins later

[Eric Edward]

I need help setting up this problem.

Black Bart is fleeing the scene of a bak robbery at 70 mph. Thirty minutes after he leaves, a police helicopter leaves the scene to catch him, traveling 100 mph along the same route. How many hours will Bart have been traveling when the police catch up?

 

[stapel]

Black Bart is fleeing the scene of a bak robbery at 70 mph. Thirty minutes after he leaves, a police helicopter leaves the scene to catch him, traveling 100 mph along the same route. How many hours will Bart have been traveling when the police catch up?

Are you familiar with the equation "d = rt"?

Thank you!

Eliz.

 

[Eric Edward]

yes but Im not sure what to do next

 

[mmm4444bot]

yes but Im not sure what to do next

Draw a picture, and understand the given situation.

There are different approaches to solve this exercise. What follows is one of these methods.

Realize that what the exercise asks for equals the sum of one-half hour PLUS the length of time (in hours) that the helicopter flew.

Realize that we can solve the equation d = r*t for t, thus obtaining an expression for time in terms of distance and rate.

Imagine that you are the pilot of the helicopter. As you pass over the bank, you start a stop watch. In other words, t = 0 at the instant you pass the bank.

Where is BB at this point in time? I mean, how far away from the bank (in miles) is BB at time t = 0?

Use the relationship d = r*t to calculate this distance.

Here's my quick sketch which is not proportional. (Double-click image to expand, if necessary.) The black dots show the relative positions of the car and helicopter at the instant you start the stop watch.

[attachment=0:2pq7d7lq]junk114.JPG[/attachment:2pq7d7lq]

Notice that d does not represent the total distance flown by the helicopter. I chose d to represent the remaining driving distance for BB from t = 0 until the helicopter catches up. When you catch up to BB, you stop the stopwatch. The amount of elapsed time, plus the additional 30 minutes, is what the exercise asks for.

Since this elapsed time is the same for both BB and you (in the helicopter), we can write an equation by expressing t in terms of distance and rate for both the car and the helicopter and setting these expressions equal to one another.

So, write an expression for t in terms of the distance traveled by the car (d) and the rate of the car (70).

Write another expression for the same t, but now express it in terms of the distance traveled by the helicopter and the rate of the helicopter.

Set these expressions equal to one another; you will have an equation containing the variable d.

Solve for d.

Once you know the value of d, you can find the value of t. This value is the length of time (in hours) that you flew from the bank to BB. Since the exercise requires BB's total driving time, you need to increase the value of t to account for BB's head start.

Please show your work if you need more help on this exercise, and try to say something about why you're stuck.

Cheers,

~ Mark