# algebra

• Mar 8th 2009, 04:08 AM
smmmc
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.
• Mar 8th 2009, 11:42 AM
earboth
Quote:

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.
• Mar 8th 2009, 03:33 PM
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
• Mar 8th 2009, 11:58 PM
earboth
Quote:

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:

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

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

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

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

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

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

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

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

Ben: $d_J=70\frac{km}{h} \cdot \left(\dfrac47 \cdot \dfrac{14}{15}\right)\ h = \dfrac{560}{19}\ km\approx 29\ km$
• Mar 9th 2009, 02:27 AM
smmmc
hey thanks

but where did you get the 14/15 from?
• Mar 9th 2009, 02:41 AM
earboth
Quote:

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 $\dfrac{14}{19}$ - but the result is correct (compare the denominators!)