Let's denote the walking speed of Paula as "P" in km/hour, and the walking speed of Malcolm as "M" in km/hour.
We know that Paula lives 2 km farther away from the ballpark than Malcolm. So, the distance Paula needs to travel, which is 2 km longer than Malcolm's distance, can be represented as:
Distance Paula = Distance Malcolm + 2 km
Now, let's consider their respective travel times. Paula needs to get to the ballpark in 40 minutes (2:00 pm - 1:20 pm), which is 2/3 of an hour. Malcolm leaves at 1:30 pm, and they both aim to arrive by 2:00 pm, so Malcolm has 30 minutes (1/2 of an hour) to get there.
Using the formula: Distance = Speed × Time, we can set up equations for both Paula and Malcolm:
For Paula:
Distance Paula = P × (2/3) hours
For Malcolm:
Distance Malcolm = M × (1/2) hours
We also know that Distance Paula is 2 km longer than Distance Malcolm:
P × (2/3) = M × (1/2) + 2
Now, we need to find the relationship between their walking speeds:
Paula is 2 km/hour faster than Malcolm:
P = M + 2
Now we have a system of two equations:
1. P × (2/3) = M × (1/2) + 2
2. P = M + 2
We can solve this system of equations simultaneously to find the walking speed of Paula (P). Let's substitute the value of P from equation 2 into equation 1:
(M + 2) × (2/3) = M × (1/2) + 2
Now, we can solve for M:
(2/3)M + (4/3) = (1/2)M + 2
Multiply both sides by 6 to eliminate fractions:
4M + 8 = 3M + 12
Subtract 3M from both sides:
M = 4
Now that we know Malcolm's walking speed (M) is 4 km/hour, we can find Paula's walking speed (P) by using equation 2:
P = M + 2
P = 4 + 2
P = 6 km/hour
So, Paula can walk at a speed of 6 km/hour.