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Sixth grade winter vacation garden math problem!
1. Method 1: Basic thinking method

The speed of cycling is (one-eighth) of the train speed and (one-fourth) of the car speed.

So cycling takes two days by bus and train 1 day every eight days.

Set [bike 8 days, car 2 days, train 1 day] to 1 group.

1 group is 1 1 day,

22 is twice as much as 1 1.

So there should be two groups,

Cycle: 8× 2 = 16 (days)

Driving: 4× 2 = 8 days

By train: 1× 2 = 2 (days)

Method 2: One-dimensional linear equation

Suppose it takes x days by train, 2x days by car and 8x days by bike. The speed of cycling is the speed of the train.

From the meaning of the question, X+2x+8x = 22 * * * 22 days ........... (one eighth) is a car.

............................................. velocity with X = 2 (one quarter).

So 2x = 2x2 = 4.

8x=2×8= 16

Method 3: ternary linear equation

It takes x days to ride a bike, y days to drive and z days to take a train.

X+Y+Z = 22 * * * The meaning of the distance problem is still 22 days.

X = 2y ... The speed of riding a bike is eight times that of a train.

X = 8z... 1), which is (a quarter) of the speed.

X = 16。

y=4

z=2

2. Method 1: Binary linear equation

Set the fast speed x (km/h) and the slow speed y (km/h).

The total distance of equation 6x = 8y is equal.

2 (x+y) = 280 2h * * * Line 280km

The result is x = 80.

y=60

The distance between the two places can be obtained by speed × time = 80× 6 = 480 (km).

Method 2: One-dimensional linear equation (complex number)

Let the total distance be x (km)

2[ 1/6 (score, one sixth, the same below) x+ 1/8x] = 280.

Note: 1/6x is the speed of A train (it takes 6 hours for the express train to go from A to B), 1/8x is the speed of B train (it takes 8 hours for the local train to go from B to A), and 2 (1/6x+ 1/8x) means that A and B travel for 2 hours.

The result is x = 480.

Method 3: Basic thinking method

It takes six hours for the express train to go from A to B, so the total distance of the express train per hour is 1/6.

It takes 8 hours for the local train to go from B to A, so the total distance of the local train per hour is 1/8.

1/6+ 1/8=7/24,

In other word, that total distance traveled by express train and local trains per hour is 7/24,

If two cars drive 280 kilometers in two hours, it is 140 kilometers/hour.

That is, 7/24 of the total distance is 140km,

Then the total distance is: 140 ÷ (7/24) = 480 (km).