Can someone help me the below two question, sorry i do not have the answer.

1) Tom and Gary ran in a race. When Gary had completed the run in 20 minutes, Tom had only run 5/8 of the distance. Tom's average speed for the race was 75m/min less than Gary's. (a) Find the distance of the race (b) What was Tom's speed in m/min?


2)Minghua and his sister had 25 sisters altogether at first. After their mother had given them some stickers, Minhua had 5 times the number of stickers he had before and his sister had 3 times the number of stickers she had before. They had a total of 95 stickers in the end. HOw many stickers did their mother give each of them?

I think this is how it is done - Problem 2:

minhua = x stickers at first
sister = y
x+y=25
After mom gave
Minhua = 5x
Sister = 3y
5x+3y=95
Mom gave 95-25=70 stickers altogether

Solving for x, we get x=10 and y=15
Thus, 5x=50, but he had 10 at first so mom gave him 50-10=40stickers
Sister =3y = 3X15=45, but she had 15 at first so mom gave her 45-15 = 30stickers

I hope this is right:)

yeah i agree. i always use algebra method for hard questions

Problem 1
1) Gary -> 20min
1 min = 1/20 D (distance)-> 16/320
Tom -> 5/8 -> 20/32
1 min = 1/32 -> 10/320

16/320 - 10/320 = 6/320
6 u = 75
1 u=12.5
320u =4000
Thus, Distance of race = 4000m
b)
12.5X10= 125m/min
Tom's speed = 125m/min

Minghua and his sister had 25 sisters altogether at first. After their mother had given them some stickers, Minhua had 5 times the number of stickers he had before and his sister had 3 times the number of stickers she had before. They had a total of 95 stickers in the end. HOw many stickers did their mother give each of them?

For question 2, I would use Simultaneous Equations (algebra) as well. But this is not because it is hard but because of the type of question. In fact, this question is actually quite easy using Simultaneous Equations. You will notice that for this question there are two equations and two unknowns. Thus, Simultaneous Equations would be appropriate.

5M + 3S --> 95
1M + 1S --> 25
3M + 3S --> 75 (multiply by 3 and subtract)

2M --> 20
1M --> 10

10 + 1S --> 25
1S --> 15

Mother gave
M --> 5x10 - 10 --> 40 stickers
S --> 3x15 - 15 --> 30 stickers

1) Tom and Gary ran in a race. When Gary had completed the run in 20 minutes, Tom had only run 5/8 of the distance. Tom's average speed for the race was 75m/min less than Gary's. (a) Find the distance of the race (b) What was Tom's speed in m/min?

Correction!

a)Distance 200m/m x 20min = 4000m not 1600m

mmmm .... yeah such a terrible mistake to make

I have updated the image to reflect the correct calculation

hi all, thanks for your assistance.