Thank you for your help.
1) After 20 minutes in a cross-country race, Seng has run 5/8 of the route while Beng has covered only 3/8 of the distance. Both run at a uniform average speed and Beng runs 60m/min slower than Seng.
(a) Find the total distance of the race.
(b) If Beng wants to finish at the same time as Seng, by how much should he increase his average speed for the remainder of the race? Express the answer in m/min
2) A class of 40 pupils helped to carry bundles of old newspapers in an event organised to collect funds for the old folks. Each boy carried 3 stacks of newspapers and each girl carried 2 stacks. Altogether, the boys carried 30 more stacks than the girls. What is the ratio of the number of boys to the number of girls in the class?
1) After 20 minutes in a cross-country race, Seng has run 5/8 of the route while Beng has covered only 3/8 of the distance. Both run at a uniform average speed and Beng runs 60m/min slower than Seng.
(a) Find the total distance of the race.
(b) If Beng wants to finish at the same time as Seng, by how much should he increase his average speed for the remainder of the race? Express the answer in m/min
1 a) Beng runs at 60m/min slower
So after 20 minutes, he ran 60m * 20 = 1200 m less than Seng
This is 5/8 - 3/8 = 2/8 of the distance
2/8 => 1200
1/8 => 600
8/8 => 4800
So the total distance of the race is 4800 m
b) Beng's average speed is 3/8 * 4800 / 20 = 90 m / min
Seng's average speed is 90+60 = 150 m / min
Seng will cover remainder of 3/8 distance (1800 m) in 1800/150 = 12 mins
Beng has 4800 - 1800 = 3000m left to cover in 12 mins
Thus, he needs a speed of 3000 / 12 = 250 m / min
So he need to increase his speed by 250 - 90 = 160m / min
2) A class of 40 pupils helped to carry bundles of old newspapers in an event organised to collect funds for the old folks. Each boy carried 3 stacks of newspapers and each girl carried 2 stacks. Altogether, the boys carried 30 more stacks than the girls. What is the ratio of the number of boys to the number of girls in the class?
Not sure if P6 learned basic algebra, but from what I have seen so far, maybe...
Let ratio of boys to girls be x : 40 - x
so 3x - 2(40 - x) = 30
5x - 80 = 30
5x = 110
x = 22
so ratio is 22:18