Answer:
Total time = 2hrs
Step-by-step explanation:
Firstly, to outline some variables, with which we can construct some equations:
x = the time taken to cross the river at 10mph (in hrs)
y = the time taken to cross the river at 5mph (in hrs)
t = total time taken to cross the river (in hrs)
a = distance travelled at speed 10mph (in miles)
b = distance travelled at speed 5mph (in miles)
Then,
a + b = 15
t = x + y
y = ¹/₂(t) ∴ t = 2y, so,
x + y = 2y ∴ x = y
Secondly, we know speed = distance/time, so,
10 = a/x ⇒ x = a/10
5 = b/x ⇒ x = b/5
So,
a/10 = b/5 ∴ a = 2b
Thirdly, if a + b = 15, then,
2b + b = 15 ⇒ 3b = 15 ⇒ b = 5
[a = 2b ∴ a = 10]
Fourthly, x = b/5, so,
x = 5/5 = 1,
Since x = y, y = 1 and since t = 2y,
t = 2(1) = 2
The whole trip, therefore, took 2hrs.
