HELP ME TO SOLVE THIS MATH QUESTION, PLEASE?

[Anonymous]

Can you help me with these math questions and provide solution? Thanks

1. If the average speed of an MRT train is 90kph, find the time it takes to travel from one station to another if the distance between the station is 6km.

2. An express train leaves one station at 6:18am and arrive at the next station at 6:24am. Find the average speed of the train, in kph. If the distance traveled is 8.4km.

3. A motorist averaged 75kph in going a distance of 300 km. He made the return trip over the same distance in 6 hours. Find his average speed for the entire trip.

4. If 2x + y + z = 21 and x + y + z = 9, then x = ?

5. If x is 150% of y, then y is what percent of x + y?

[saffoler]

1. Take the distance and divide it by the average speed, 6km / 90km/hr. That gives you.066666667 hours which converts to 4 minutes (.06666667*60).

2. First subtract 6:18 from 6:24 to find the time it took to travel the distance, 24-18. This is 6 minutes. Then divide the distance by the time, 8.4 km / 6 min. This gives you an average speed of 1.4 km/min which converts to 84 KPH (1.4*60).

3. First find the time it took the first part of the trip by dividing the distance by the speed, 300km / 75 km/hr. This gives us 4 hours. Now add the two times and double the distance, 4hr + 6hr and 300km * 2. We get 10 hours and 600 km. Now divide the distance by the time, 600km / 10hr. And we end up with 60km/hr.

4. Since we have two equations and three unknowns; we are at an impass unless we utilize the substitution method. In this case we will substitute y+z for a. That way we have 2x + a = 21 and x + a =9. Now that we have the same number of equations as unknowns we can solve for x. Taking the second equation x + a = 9; we will subtract x from both sides, x + a - x = 9 - x. Which simplifies down to a = 9 - x. Now we can replace a in the first equation with 9 - x; which gives us 2x + 9 -x = 21. Then we subtract 9 from both sides. 2x + 9 - x - 9 = 21 - 9; that simplifies to 2x - x = 13, and again to x = 13.

5. So x is 150% of y and y is 100% of y. If you add x + y or 150% + 100%; you get 250%. Then you divide 100% by 250%, 100 / 250. Which comes out to.4 or 40% (.4*100).

Hope that helps explain how to solve those equations.

[Avicenna]

Number one is four minutes