Speed of the boat = u
speed of the current = v
in downstream,
u - v = 105/5
u - v = 21
in upstream
u + v = 105/7
u + v = 15
add both equations
2u = 36
u = 18
v = -3
so
speed of the boat = 18 km/h
speed of the current = 3 km/h
Hi there! 3 feet = 1 yard, 12 inches = 1 foot and 36 inches = 1 yard. All we have to do is change them up into different units by doing a bit of multiplication, division, maybe mental math, and even proportions if you know how to do them. Regardless on what you do, if you do it correctly, here are what your answers should be for each unit.
Inches
Carol: 42 inches
Tino: 30 inches
Baxter: 54 inches
Feet:
Carol: 3.5 feet
Tino: 2.5 feet
Baxter: 4.5 feet
Yards:
Carol: 1 1/6 yards
Tino: 5/6 yards
Baxter: 1 1/2 yards
Answer: a) P = 0.5, b) P = 0.07
Step-by-step explanation:
Hi!
Lets call X₁ the time at which you arrive, and X₂ the time at which Bob arrives. Both are random variables with uniform density in the interval [0, 60] (in minutes). Their joint distribuition is uniform over the square in the image, with value P = 1/(60*60) = 1/3600.
a) For you to get more cake than Bob, you should arrive earlier. This event is A = { X₁ < X₂ }, the shaded triangle in the figure.The area of this event (set) is half the total area of the square, so P(A) = 0.5.
It makes sense, beacuse its equally probable for you or Bob to arrive earlier, as both have uniform density over the time interval.
b) In this case you arrive later than Bob, but less than 5 minutes later. So the event is B = { X₂ < X₁ < (X₂ + 5) } . This is the gray shaded area in b) part of the image. Its area is the difference two triangles (half square - blue triangle), then the probability is:
