Algebra 1 problems

Question

Please help me with these problems and could you show all the steps?

 

1. A jet leaves the airport traveling at a speed of 560 km/h. Another jet, leaving the same airport and traveling in the same direction, leaves 45 minutes later traveling at 750 km/h. About how long will it take for the second jet to overtake the first jet?

 

2. Bus A leaves Eastport at 7 a.m. at a speed of 40 km/h and is bound for Westport. Bus B leaves Eastport at 7:45 a.m. and drives along the same freeway at 50 km/h. Bus C leaves Westport at 7:45 a.m. traveling towards Eastport along the same freeway at 60 km/h. Westport and Eastport are 220 km apart. Will bus B or bus C pass bus A first?

Answer 1

If Bus B and Bus C leave Eastport at the same time and bus C is faster than bus B, is obvious that C will pass bus A first. The equation will be 40(t-7) = 60(t-7.75) 45 min are 0.75 of an hour. Solving this equation for t, we obtain t= 9.25 = 9:15 => we may conclude that after (9.25 - 7.75) = 1.5 hours of leaving Bus B will pass bus A. After bus C running for 90 kilometers this will happen. To test, bus 1 will have run (9.25-7)= 2.25 hours and the distance is 90 kilometers.

Problem 1 is similar and the equation is

(t-0)*560 = t(-45)*750, solve for t and get the time when this happens.

Answer 2

Let me go ahead and help you start on these questions...

Question 1:

From the question we can see that we are talking about 2 jets, but we only are concerned with a single variable.  Can you tell me the variable?

 

Time!  

Let t = time that the plane was in flight in hours

 

This means we can write a single equation, because we only need a single variable!  Let's try to relate the distance of each plane to each other.  

 

**Remember: Distance=Rate x Time

 

Setting up the Equations:

Plane 1 becomes : 560t  rate=560 x time=t

 

Plane 2 becomes : 750 ______  

 

**try to fill in the blank, think how can we represent 45 minutes later(hint: 45 mins is 45/60 hours)?  I'll be happy to check it over if you email me directly or leave a comment here.

 

Now What...

After you fill in the blank, it's pretty easy from there...the planes will meet each other when the equation for plane 1 is equal to the equation for plane 2!  Set the two equations equal then solve for the variable "t".  This is the amount of time it will take for plane 2 to catch up to plane 1!  Easy Breezy

 

Andrew L.'s Final Thoughts:

 

After we make some progress on question 1, I'll be happy to walk you through question 2.  It is very important that you can understand how one represents "45 minutes later" mathematically.  Regent exams love to test this and it will definitely come in handy in more advanced math courses.  I look forward helping you understand these questions!  Talk to you soon.