1. ## algebra

1) Jack cycles home from work, a distance of 10x km. Benny leaves at the same time and
drives the 40x km to his home.
A. If Jack and Benny arrive at their homes 30 minutes apart
i. find x, correct to three decimal places
ii. find the distance from work of each home, correct to the nearest kilometre.

2. Originally Posted by smmmc
1) Jack cycles home from work, a distance of 10x km. Benny leaves at the same time and
drives the 40x km to his home.
A. If Jack and Benny arrive at their homes 30 minutes apart
i. find x, correct to three decimal places
ii. find the distance from work of each home, correct to the nearest kilometre.
Are you certain that this is the complete question? In my opinion we need a value of the speed with which the two are going.

3. this is it
1. Jack cycles home from work, a distance of 10x km. Benny leaves at the same time and
drives the 40x km to his home.
a. Write an expression in terms of x for the time taken for Jack to reach home if he cycles
at 8 km/h on average.
b. Write an expression in terms of x for the time taken for Benny to reach home if he
drives at an average speed of 70 km/h.
c. In terms of x, find the difference in times of the two journeys.
d. If Jack and Benny arrive at their homes 30 minutes apart
i. find x, correct to three decimal places
ii. find the distance from work of each home, correct to the nearest kilometre.

im stuck on d

4. Originally Posted by smmmc
this is it
1. Jack cycles home from work, a distance of 10x km. Benny leaves at the same time and
drives the 40x km to his home.
a. Write an expression in terms of x for the time taken for Jack to reach home if he cycles
at 8 km/h on average.
b. Write an expression in terms of x for the time taken for Benny to reach home if he
drives at an average speed of 70 km/h.
c. In terms of x, find the difference in times of the two journeys.
d. If Jack and Benny arrive at their homes 30 minutes apart
i. find x, correct to three decimal places
ii. find the distance from work of each home, correct to the nearest kilometre.

im stuck on d
Use the definition:

$\displaystyle speed = \dfrac{distance}{elapsed \ time}~\implies~elapsed\ time = \dfrac{distance}{speed}$

a) d = 10x km, s = 8 km/h, therefore $\displaystyle t_J=\dfrac{10x}8=\dfrac54 x$

b) d = 40x km, s = 70 km/h, therefore $\displaystyle t_B=\dfrac{40x}{70}=\dfrac47 x$

c) $\displaystyle \Delta(t)=t_J - t_B = \dfrac{19}{28} x$

d) 30 min = 0.5 h that means: $\displaystyle \Delta(t)= \dfrac12$

$\displaystyle \dfrac{19}{28} x = \dfrac12~\implies~x = \dfrac{14}{19} \approx 0.737$

From the definition given above you get: $\displaystyle distance = speed \cdot elapsed\ time$

Jack: $\displaystyle d_J=8\frac{km}{h} \cdot \left(\dfrac54 \cdot \dfrac{14}{15}\right)\ h = \dfrac{140}{19}\ km\approx 7\ km$

Ben: $\displaystyle d_J=70\frac{km}{h} \cdot \left(\dfrac47 \cdot \dfrac{14}{15}\right)\ h = \dfrac{560}{19}\ km\approx 29\ km$

5. hey thanks

but where did you get the 14/15 from?

6. Originally Posted by smmmc
hey thanks

but where did you get the 14/15 from?
It's one of my silly typos: Actually it is $\displaystyle \dfrac{14}{19}$ - but the result is correct (compare the denominators!)