Expert: Scott A Wilson - 5/18/2010

Question
QUESTION: 1) Martin leaves 10 kilometers from school. If he rides his bike at 12 kph and leaves the school at 2:00 pm, what time will he reach home?

2) A car leaves a gasoline station at 60 kph. How long will a second car traveling at 75 kph to catch the first car if it leaves the same station 1 hour later?

3)Two cars leave two towns that are 230 kilometers apart at the same time, traveling directly to each other. One car travels 15 kilometers per hour slower than the other. They pass one another 2 hours later. What are their speeds?

 4) In a marathon, Janet runs the speed of 5 kph. Paula leaves 10 minutes after Janet and runs at 6 kph. How long will it take for Paula to catch up with Janet?

   5) On an automobile trip, Jessa maintained a steady speed for 30 minutes. Rush hour traffic slowed her speed by 40 kph for the last part of the trip. The entire trip, a distance of 38 kilometers, took 1 hour and 15 minutes. What was her speed during the first part  of the trip?

   6) Two planes leave Mactan International airport at the same time. One travels north at 680 miles per hour and the other travels south at 620 miles per hour. How long will it take for the two planes to be 3900 miles apart?

 Note: Please answer these questions like this. Example: Let x be the no. of hours......  First car 30x second car 24 Use the ALGEBRA WAY! And If you can't answer all, maybe one answer will help a lot. thanks!

ANSWER: 1) If there are 10 k and he travel as 12k/h, it will take 10/12 of an hour.
Multiply by 60 to get minutes.  Note that 60/12 = 5.

2) In 1 hour, the 1st car travels 60 kilometers.
The second car is travelling 15 k/h faster than the 1st car, so the time is 60/15 = ...

3) Distance = 230 km.
Travelling towards each other means determine how fast 230 km can be when adding the speeds together.  Thus, using d = rt, it is known that d = 230, r = x + x-15 = 2x - 15, and t = 2.

4) In 10 minutes, Janet went 5/6 of a kilometer at 5 kph.
If Paula is travelling at 6 kph, that's only 1 kph faster.
But anyway, for Janet the distance is 5t + 5/6 and for Paula is is 6t.
Set these equal and solve for t.

5) Take velocity at the start as v.  This means at the end, it was v-40.
Since the first part took 30 minutes, and the entire trip took 75 minutes,
this means the 2nd part took 75-30=45 minutes.

In hours, this is 1/2 and hour and 3/4 of an hour.
That means 38 = v/2 + (v-40)(3/4).

6) Since travle is in opposite directions, add the speeds together.  This gives 690+620=1300.
That answer would be found by solving 1300t = 3900, giving t in hours.


---------- FOLLOW-UP ----------

QUESTION: 1) THE LENGTH OF A RECTANGLE IS 5 MORE THAN TWICE ITS WIDTH. IF THE WIDTH IS DECREASED BY 3 AND THE LENGTH BY 1, THE PERIMETER BECOMES FOUR-FIFTHS OF THE ORIGINAL. FIND THE ORIGINAL DIMENSIONS OF THE RECTANGLE.

2) THE COMPLEMENT OF AN ANGLE MEASURES 10 LESS THAN ONE-FIFTH OF ITS SUPPLEMENT. FIND THE MEASURE OF THE ANGLE.

Answer
1) It is known that P = 2(W+L) and the L = 2W + 5.

If the width is decreased by 3 and the length by 1, this decreases the perimeter by 2(3+1) = 8.

The equation to solve is then 4P/5 = (P-8).

This eqution can be solved for P.

The equation for L = 2W + 5 can be put into the equation P = 2(W+L) so we have P as a function of W alone.

Since P was found above, W can be found, and then L.

2) The measure of angle will be called A.
The measure of the complement of that angle is 90-A.
The measure of the supplement of that angle is 180-A.

The equation generated is 90° -  A° = (1/5)(180-A)° - 10°.
The measure of angle A comes out to be a multiple of 10°.