Another one about the Systems of Linear Equations in Two Variables?

Question

37. A boat goes downstream a distance of 5 mi in 15 min, but it takes 20 min for the return trip. Find the rate of the boat in still water and the rate of the current.

38. An airplane travels a distance of 1980 mi in 6 hr with the wind, but it takes 20 min for the return trip. Find the rate of the airplane in still air and the rate of the wind.

39. It takes a man 23 min longer to jog 5 mi than it takes his son to run the same distance. However, if the man doubles his rate, he can run the distance in 1 min less than his son. What is the man’s rate of jogging and what is his son’s rate of running?

40. The distance between two automobiles is 140 km. If the cars are driven toward each other, they will meet in 48 min. However, if they are driven in the same direction, they will meet in 4 hr. What is the rate at which each car is driven.

Answer 1

*sigh* ok

(37)
Boat goes 5 mi in 15 mins WITH the current
but comes back 5 mi in 20 min against the current

Speed s + c = 5/15
s - c = 5/20

2s = 1/3 + 1/4

s = 7/24 mi/min in still water

c = 5/15 - 7/24
= (24x5 - 15x7) / (15x24)
= (120-105) / 360
= 1/24

Check
s - c = 7/24 - 1/ 24
= 6 /24
= 1/4 = 5mi / 20min = RHS

(38) Same idea

(39) man jogs at x, son runs at y
s = d/t
t = d/s

5/x = 5/y + 23

5/2x + 1 = 5/y

rearrange eqn 1
5/y = 5/x - 23 = 5/2x + 1
5/x = 5/2x + 24

5/x - 5/2x = 24
10/2x - 5/2x = 24
5/2x = 24
2x = 5/24
x = 5/48

plug it in and solve for y

check

(40)
first car travels at x km/h (faster car)
next car travels at y km/h
x + y covers 140km in 48 min or 4/5 of an hr

but ... driving in the same direction they arrive at the same point in 4 hours.

Car y has covered 4y km

Car x has covered 4x km but this is the same as 4y+140

4x = 4y+140
4x - 4y = 140

4x + 4y = 3.2
8x = 143.2
x = 17.9km/h

plug this in to above equation and solve for y

check

Answer 2

draw the two strains on paper via springing up 2 factors for each for y=x, plug in 2 values of x so x=0, y additionally will = 0 x=a million, y=a million so plot 2 factors (0,0) and (a million,a million) for y=3x-3, x=0 y=-3 and x=a million, y=-2 plot 2 factors (0,-3) and (a million,-2) draw a line via starting to be a member of the two factors for each graph and make larger them till they meet the place the two strains intercept provides you with the answer

Answer 3

dont you even try to do your H.W???