1. Jodie biycles 5km/h faster than Predup. In the same time it takes Predup to bicycle 60km, Jodie can bicycle 75km. How fast does each bicyclist travel?

2.The officejet printer can copy Janet's dissertation in 20min. The LaserJet printer can copy the same document in 14min. If the two machine work together ,how long would they take to copy the dissertation.

j=p+5

60/p = 75/j

60/p = 75/p+5
60p + 300 = 75p
15p = 300
p=20
so, j=25

60/20 = 75/25
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Let b be the time it takes both machines together

1/b = 1/20 + 1/14 = 34/280
b = 280/34 = 140/17

1. Let's assume the speed at which Predup bicycles is x km/h. Since Jodie bicycles 5 km/h faster, Jodie's speed would be (x + 5) km/h.

We are given that Predup takes the same time to travel 60 km as Jodie takes to travel 75 km. We can use the formula: Distance = Speed × Time.

For Predup: Distance = 60 km, Speed = x km/h, Time = (60 km / x km/h) = 60/x hours.
For Jodie: Distance = 75 km, Speed = (x + 5) km/h, Time = (75 km / (x + 5) km/h) = 75/(x + 5) hours.

Since both Predup and Jodie take the same time, we can set up the equation: 60/x = 75/(x + 5).

To solve this equation, we can cross multiply:
60(x + 5) = 75x.

Expanding and simplifying the equation:
60x + 300 = 75x,
300 = 75x - 60x,
300 = 15x.

Dividing both sides of the equation by 15:
x = 20.

Therefore, Predup bicycles at a speed of 20 km/h, and Jodie bicycles at a speed of (20 + 5) = 25 km/h.

2. Let's assume the time it takes for the Officejet printer to copy Janet's dissertation is x minutes. Similarly, let's assume the time it takes for the LaserJet printer to copy the same document is y minutes.

We are given that the Officejet printer takes 20 minutes and the LaserJet printer takes 14 minutes to copy the dissertation. Therefore, we have the following equations:

20 minutes = x,
14 minutes = y.

Now, we need to determine how long it would take if the two machines work together. We can use the concept of work done per unit time. The work done by the Officejet printer in 1 minute is 1/x, and the work done by the LaserJet printer in 1 minute is 1/y. When they work together, their combined work done in 1 minute is 1/x + 1/y.

To find the time it would take for them to copy the dissertation together, we can set up the equation: (1/x) + (1/y) = 1/t, where t represents the time in minutes.

Substituting the known values:
(1/20) + (1/14) = 1/t.

To solve this equation, we can find the least common denominator (LCD) of 20 and 14, which is 140.
Multiply both sides of the equation by 140t:
(140t/20) + (140t/14) = 140.

Simplifying:
7t + 10t = 140,
17t = 140.

Dividing both sides of the equation by 17:
t = 140/17.

So, if the Officejet and LaserJet printers work together, they would take approximately 8.24 minutes (rounded to two decimal places) to copy the dissertation.