Math word question?

I get total brain farts when it comes to word problems, and it would help greatly to see these practice problems worked out.





1) The distance between city A and B is 2800 mi. On a certain map, this distance is repredented by 140 inc. On the same map, city C and city D are 88 in. apart. What is the actualy distance between city C and city D?





2) Paul Nagel invested some money at 3.5% simple interest and $1000 more than that amount at 5% simple interest. After 1 year, his total interest from the two accounts were $560. How much did he invest at each rate?





3) From a point on a straight road, two cars are driven in opposite directions, one at 42 miles per hour and the other at 38 miles per hourr. In how many hours will they be 240 miles apart?





Thanks.

Math word question?
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2800mi / 140in = 20 mi/in


(20 mi/in) x (88 in) = 1760 miles


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3.5% rate = 0.035x


5.0% rate = 0.05(x + 1000)





.035x + 0.05(x + 1000) = 560


0.035x + 0.05x + 50 = 560


.085x = 510


x = 6000





$6000 @ 3.5%


$7000 @ 5%


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38mph + 42 mph = 80mph total





240mi / 80mph = 3 hours
Reply:1. 88 times 140 = whatever in inches, and make sure you re-write it in miles to be compatible with actual distance





(no one says the distance between two cities are several inches LOL)





2. formula for interest should be I= prt


I = amount after the investment timing


in this case, we dont know how much at the end of the investment after one year, but we do know that the total interest gained is 560, so total interest 560 Plus unknown principle (the starting amount) wll give us the total at the end of one year investing =)





p= principle (in this case unknown)


r= interest level


t=how many years invested





so here we go:


x+ 560 = (x times 3.5% times 1year) + ( (x+1000)times 5% times 1 year)





now solve for x





3. this one is actually quite easy


42 x + 38 x= 240


x is the number of hours driving





solve for x





good luck
Reply:1) is a ratio question so map it out (no pun intended)


A-B is 2800:140


so C-D is x:88 and solve by cross multiplication


140x=2800(88)





2) You need to create equations and solve for a common.


1st: x(3.5/100)=y


2nd: (x+1000)(5/100)=z


y+z=560, then substitute the x fator equations and solve for x.





3) Add their speed rates together, ie 38+42=x, then divide 240 by x and there's your answer.
Reply:1.) you set up 140/2800=88/x and then you cross multiply to get 140x=246400 then you divide to get x=1760 that is how you do that.





2.) 0.05*1000=50 and 560-50=510 so 3.5/x=510 then multiply 510 by 3.5 to get x which =1785





3.)guess and check


3 hours because 42*3=126 and 38*3=114 and 114+126=240miles