could you please show me how to do this
problem? Bob rows 6 miles downstream in 1 hr, joe rows 6 miles upstream in 2 hr. joe rows 1 mile per hour faster.
a. what is each of their speed, bob 6/1=6mph joe 6 + 1 = 7mph is this right??
b. what is the current speed??
downstream R + c = 6/1 6mph
upstream R-C 6/2 = 3mph
6-3/2 = 3/2 or 1 1/2 mph current speed
c. if bob and joe rowing separately , who would complete trip first and by how long.
thank you
a. Vb + Vc = 6.
Vb - Vc = 6/2-1 = 2.
Add the two Eqs:
Eq1: Vb + Vc = 6.
Eq2: Vb - Vc = 2.
2Vb= 8.
Vb = 4 Mi/h = Velocity of Bob's boat.
Joe: Vb = 4 + 1 = 5 Mi/h.
b. In Eq1, substitute 4 for vb:
4 + Vc = 6.
Vc = 6 - 4 = 2 Mi/h = Velocity of the current.
c. Bob: T1 + T2 = 6/6 + 6/2 = 4 hrs.
Joe: 6/7 + 6/3 = 2 6/7 = 2.86 Hrs.
Margin = 4-2.86 = 1.14 hrs.
thank you very much henry , I really appreciate the help. ann
a. Yes, you are correct. Bob's speed is 6 mph, as he rows 6 miles downstream in 1 hour. Joe's speed is 7 mph, as he rows 6 miles upstream in 2 hours and he rows 1 mile per hour faster than Bob.
b. To find the current speed, we can use the formula:
Downstream Speed (R + c) = Distance / Time
Substituting the values given, we have:
6 mph = 6 miles / 1 hour
Therefore, the downstream speed is 6 mph.
Similarly, using the formula for the upstream speed:
Upstream Speed (R - c) = Distance / Time
Substituting the values given, we have:
3 mph = 6 miles / 2 hours
Therefore, the upstream speed is 3 mph.
To find the current speed, we can use the formula:
Current Speed (c) = (Downstream Speed - Upstream Speed) / 2
Substituting the values we found earlier, we have:
c = (6 mph - 3 mph) / 2
Therefore, the current speed is 1.5 mph or 1 1/2 mph.
c. To determine who would complete the trip first, we need to compare the times it takes for each person.
Bob's time to complete the trip downstream is 6 miles / 6 mph = 1 hour.
Joe's time to complete the trip upstream is 6 miles / 7 mph ≈ 0.857 hours or approximately 51.43 minutes.
Therefore, Bob would complete the trip first, with a time advantage of approximately 8 minutes and 34 seconds (60 minutes - 51.43 minutes).
So, Bob would complete the trip first, with a time advantage of approximately 8 minutes and 34 seconds.