Tough algebra question... please help!!! :)?

Question

both a read leading to a bridge and the bridge must be replaced. the engineer estimates that it will take 20 days for the road crew to tear up and clear the road and an additional 60 days for the same road crew to dismantle and clear the bridge. the rate for clearing the road is 1.2 feet per day faster than the rate for clearing the bridge and the total distance is 124 feet. find the rate for clearing the road and the rate for clearing the bridge

Answer 1

Edit: Sorry, had to edit as I was at first confused
whether 'faster' meant to multiply or to add the 1.2.
I'm more sure now that it needs to be added.

Let R = rate for clearing the road (ft/day).
Let B = rate for clearing the bridge (ft/day).
It is given that R = B + 1.2.
Let D1 = length of road, and D2 = length of bridge.
It is given that D1 + D2 = 124 feet.

Now we can use the formula: distance = speed * time,
or what is the same thing: distance = rate * time.

For the road, we have: D1 = R * 20
But R = B + 1.2, so D1 = (B + 1.2) * 20 = 20B + 24

For the bridge, we have: D2 = B * 60 = 60B

Adding these two equations gives:
D1 + D2 = 20B + 24 + 60B = 80B + 24
But D1 + D2 = 124, so 80B + 24 = 124

Therefore, B = (124 -24)/80 = 1.25.

and, R = B + 1.2 = 1.25 + 1.2 = 2.45

Thus, rate for clearing road = 2.45 ft/day
and rate for clearing bridge = 1.25 ft/day.

Answer 2

It's not that tough, you just need to find the equations.

Let x be the rate of clearing the road.
Let y be the rate of clearing the bridge.

We know:
y = x - 1.2
20*x + 60*y = 124

Plug the y-value from the first equation into the second:
20*x + 60*(x-1.2) = 124

You can solve it from there.

Answer 3

a = length of road
b = length of bridge
c = rate of clearing road
d = rate of clearing bridge

Given
a + b = 124 feet
c = d + 1.2 feet/day
20 days = time to clear road
60 days = time to clear bridge

We have

124 = 20c + 60d = 20(d + 1.2) + 60d = 20d + 24 + 60d = 80d + 24
100 = 80d
d = 5/4 = 1.25 ft/day
c = d + 1.2 = 1.25 + 1.2 = 2.45 ft/day

The rate of clearing the road is 2.45 ft/day and the rate of clearing the bridge is 1.25 ft/day.